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class="jsx-5de5b851a90f387"><img src="https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-2000.jpg" alt="" srcSet="https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-2000.jpg 1920w,https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-1500.jpg 1500w,https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-800.jpg 800w,https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-600.jpg 600w,https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-400.jpg 400w,https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-300.jpg 300w" sizes="100vw" loading="lazy" class="jsx-2524453792 "/><div class="jsx-5de5b851a90f387 title hero-title"><span class="jsx-5de5b851a90f387 overline">Explore | Series</span><h3 class="jsx-5de5b851a90f387 alpha cf"><span class="jsx-5de5b851a90f387">The Fabric of the Cosmos</span></h3><div class="jsx-5de5b851a90f387 description"><p>Acclaimed physicist 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card cf" href="/wgbh/nova/video/the-hippy-days-of-quantum-physics/"><figure class="jsx-2104659082"><span class="jsx-f3c2a27e2e815a81 play-icon center"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="jsx-f3c2a27e2e815a81"><path d="M81.4 50.4q.15683594-.4 0-.85-.10527344-.40976562-.45-.7l-51.3-42.6q-.45859375-.38320312-1.05-.35-.59160156.03867187-1 .45-.40410156.45820313-.4 1.05v85.25q-.00410156.59179688.4 1 .40839844.46132812 1 .5.59140625.03320313 1.05-.35l51.3-42.65q.34472656-.29023437.45-.75z" class="jsx-f3c2a27e2e815a81"></path></svg></span><img src="https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg" alt="" srcSet="https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg 1920w,https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-1500.jpg 1500w,https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-800.jpg 800w,https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-600.jpg 600w,https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-400.jpg 400w,https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-300.jpg 300w" sizes="100vw" loading="lazy" class="jsx-2524453792 "/></figure><span class="jsx-2104659082">Watch | Short</span><h3 class="jsx-2104659082 cf"><b class="jsx-2104659082">The “Hippy Days” of Quantum Physics</b></h3><div class="jsx-2104659082 description"><p data-block-key="6mu2u">How a group of free-thinking physicists in the 1970s helped shape quantum physics.</p></div></a></article></div><div class="jsx-795ad97d004eefca results"><article class="jsx-795ad97d004eefca cf"><a class="jsx-447409963 link-reset card cf" href="/wgbh/nova/video/mystery-and-physics-of-spiral-football-pass/"><figure class="jsx-684090880"><span class="jsx-f3c2a27e2e815a81 play-icon corner"><svg 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600w,https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-400.jpg 400w,https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-300.jpg 300w" sizes="100vw" loading="lazy" class="jsx-2524453792 "/></figure><span class="jsx-684090880">Watch | Short</span><h3 class="jsx-684090880 cf"><b class="jsx-684090880">The Mystery and Physics of the Spiral Football Pass</b></h3><div class="jsx-684090880 description"><p data-block-key="zu4f7">There are two key players involved: gravity and angular momentum.</p></div></a></article><article class="jsx-795ad97d004eefca cf"><a class="jsx-447409963 link-reset card cf" href="/wgbh/nova/video/teen-calculates-mind-boggling-math-in-head/"><figure class="jsx-684090880"><span class="jsx-f3c2a27e2e815a81 play-icon corner"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 100 100" class="jsx-f3c2a27e2e815a81"><path d="M81.4 50.4q.15683594-.4 0-.85-.10527344-.40976562-.45-.7l-51.3-42.6q-.45859375-.38320312-1.05-.35-.59160156.03867187-1 .45-.40410156.45820313-.4 1.05v85.25q-.00410156.59179688.4 1 .40839844.46132812 1 .5.59140625.03320313 1.05-.35l51.3-42.65q.34472656-.29023437.45-.75z" class="jsx-f3c2a27e2e815a81"></path></svg></span><img src="https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png" alt="Apoorva Panidapu" srcSet="https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png 1664w,https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-1500.png 1500w,https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-800.png 800w,https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-600.png 600w,https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-400.png 400w,https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-300.png 300w" sizes="100vw" loading="lazy" 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src="https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png" alt="On a black background, a row of 6 red die lines up with a row of 6 red shoes, with white lines connecting them" srcSet="https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png 1920w,https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-1500.png 1500w,https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-800.png 800w,https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-600.png 600w,https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-400.png 400w,https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-300.png 300w" sizes="100vw" loading="lazy" class="jsx-2524453792 "/></figure><span class="jsx-684090880">Read | Article</span><h3 class="jsx-684090880 cf"><b class="jsx-684090880">4 mind-bending math experiments that explain infinity</b></h3><div class="jsx-684090880 description"><p data-block-key="03b0f">Can one infinity be bigger 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data-block-key=\"47aso\"\u003eThese scientists were the pioneers of quantum mechanics.\u003c/p\u003e\n\u003cp data-block-key=\"7md9n\"\u003eThe theory of quantum mechanics presented at the meeting said that a particle like an electron isn’t physically real until it’s observed, measured by an instrument that can detect it. Before it’s detected, instead of being a solid particle, an electron is just a fuzzy wave, a wave of probability.\u003c/p\u003e\n\u003cp data-block-key=\"du910\"\u003e\u003cb\u003eOne of the Greatest Meetings of the Minds in History\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"fqeho\"\u003ePublished: August 27, 2024\u003c/p\u003e\u003cp data-block-key=\"5m8hn\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e It was the nature of fundamental particles which make up the world we see around us that Einstein had come to Brussels to discuss, and it was here that Einstein entered into a heated debate that would lead to the discovery of quantum entanglement, a concept that would trouble him for the rest of his life.\u003c/p\u003e\u003cp data-block-key=\"43mcn\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e This is the original Solvay Institute building, and this is the place back in October 1927 where the fifth Solvay Conference was held. This amazing week-long series of discussions on really what the world is made of, on the nature of matter and the new quantum theory, and these steps are the very steps on which this famous group photograph was taken. It\u0026#x27;s a collection of some of the most brilliant people in the world.\u003c/p\u003e\u003cp data-block-key=\"a9d9n\"\u003eHere in the front row, we see Albert Einstein and the great Marie Curie and Max Planck. In the back row standing, the dapper Erwin Schrödinger, and these brash 20-year-olds or mid-20s, Werner Heisenberg and Wolfgang Pauli.\u003c/p\u003e\u003cp data-block-key=\"cknj8\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e These scientists were the pioneers of quantum mechanics.\u003c/p\u003e\u003cp data-block-key=\"7em10\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e I had a huge version of this photograph up on the wall. It was a poster in my college dorm room. My roommates had their favorite bands, and I had the 1927 Solvay Conference, which says a lot.\u003c/p\u003e\u003cp data-block-key=\"esp0s\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e This was one of the greatest meetings of minds in history. More than half were or would become Nobel Prize winners. Their experiments were showing that deep inside matter tiny particles like atoms and their orbiting electrons were not solid little spheres, they seemed fuzzy and undefined.\u003c/p\u003e\u003cp data-block-key=\"61slt\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e So this group here, these were the folks who had just been plumbing deeper and deeper and deeper to find what they hoped would be a bedrock of what the world is made of, and to their surprise they found things less and less solid as they dug in. This world was not tiny little bricks that got smaller and smaller. At some point, the bricks gave way to this mush, and what looked like solidity, solidness, in fact became very confusing and kind of a whole new way of thinking about nature.\u003c/p\u003e\n\n\n","passport_start":"2024-08-27T22:21:55+00:00","short_description":"\u003cp data-block-key=\"47aso\"\u003eThese scientists were the pioneers of quantum mechanics.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"One of the Greatest Meetings of the Minds in History","slug":"one-of-the-greatest-meetings-of-the-minds-in-history","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/one-of-the-greatest-meetings-of-the-minds-in-history-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1724802896958]},{"_index":"content","_type":"doc","_id":"sfv-6814","_score":null,"_source":{"slug":"the-hippy-days-of-quantum-physics","title":"The “Hippy Days” of Quantum Physics","topic":"physics","brand":"nova","content_type":"shortvideopage","length":103,"publish_date":"2024-08-27T04:24:03.009203+00:00","tags":["70s science","einstein's quantum riddle","hippy science","Fundamental Fysiks Group","1970s","70s","quantum","quantum physics","einstein"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-hippy-days-of-quantum-physics-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"6mu2u\"\u003eHow a group of free-thinking physicists in the 1970s helped shape quantum physics.\u003c/p\u003e\n\u003cp data-block-key=\"jlnbl\"\u003eIn seeing quantum entanglement as central to physics, The Fundamental Fysiks Group were decades ahead of their time.\u003c/p\u003e\n\u003cp data-block-key=\"ujdqk\"\u003e\u003cb\u003eThe “Hippy Days” of Quantum Physics\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"38qia\"\u003ePublished: August 27, 2024\u003c/p\u003e\u003cp data-block-key=\"6i67u\"\u003e\u003cb\u003eSpeaker 1:\u003c/b\u003e They call themselves the Fundamental Fysics Group, they spelled Fysics with an F. Some members would experiment with psychedelic drugs. I mean, they were in the flow of the hippie scene, and that group was just mesmerized by the question of entanglement.\u003c/p\u003e\u003cp data-block-key=\"48cms\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e The idea was just to discuss fringe subjects with an open mind, and I thought of, \u0026quot;Sure, that\u0026#x27;s kind of what I do.\u0026quot; They were doing their best to link eastern mysticism with quantum entanglement. They sold a lot of popular textbooks. There were a lot of followers.\u003c/p\u003e\u003cp data-block-key=\"6rldk\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Their books became bestsellers like The Tao of Physics, which highlighted that Eastern philosophy and quantum entanglement both described the deep connectedness of things in the universe.\u003c/p\u003e\u003cp data-block-key=\"eesa\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e It was the great cosmic oneness.\u003c/p\u003e\u003cp data-block-key=\"jgf6\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The group held meetings at the iconic Esalen Institute.\u003c/p\u003e\u003cp data-block-key=\"dq2bl\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e It was a marvelous, beautiful place where they would discuss all of these ideas. It was right on the Pacific coast with the overflow from the hot tubs cascading down the cliffs into the Pacific Ocean. To my knowledge, no useful connections to Eastern mysticism were ever discovered by the group, but it was fun.\u003c/p\u003e\u003cp data-block-key=\"d1ml8\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The Fundamental Fysics group may not have uncovered the secrets of cosmic oneness, but in seeing entanglement as central to physics, they were decades ahead of their time.\u003c/p\u003e\n\n\n","passport_start":"2024-08-27T01:00:12+00:00","short_description":"\u003cp data-block-key=\"6mu2u\"\u003eHow a group of free-thinking physicists in the 1970s helped shape quantum physics.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"The “Hippy Days” of Quantum Physics","slug":"the-hippy-days-of-quantum-physics","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-hippy-days-of-quantum-physics-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1724732643009]},{"_index":"content","_type":"doc","_id":"sfv-6593","_score":null,"_source":{"slug":"mystery-and-physics-of-spiral-football-pass","title":"The Mystery and Physics of the Spiral Football Pass","topic":"physics","brand":"nova","content_type":"shortvideopage","length":223,"publish_date":"2023-02-15T16:29:53.981920+00:00","tags":["football","physics","sports","mystery","physics in sports","spiral pass","spiral football pass"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-mystery-and-physics-of-the-spiral-football-pass-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"zu4f7\"\u003eThere are two key players involved: gravity and angular momentum.\u003c/p\u003e\n\u003cp data-block-key=\"6otjm\"\u003eThe way the spiral football pass travels through the air baffled physicists for years.\u003c/p\u003e\n\u003cp data-block-key=\"zgifh\"\u003e\u003cb\u003eThe Mystery and Physics of the Spiral Football Pass\u003cbr/\u003e\u003c/b\u003ePublished February 15, 2023\u003cbr/\u003e\u003c/p\u003e\u003cp data-block-key=\"eibhd\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The perfect football pass, a thing of beauty—and bewilderment. The way the football travels mid-air baffled physicists for years.\u003c/p\u003e\u003cp data-block-key=\"866nm\"\u003e\u003cb\u003eSteve Lamoreaux\u003c/b\u003e: If you\u0026#x27;re in the physicist\u0026#x27;s world, you expect a football to travel like this and come down. When you watch a long pass from a talented quarterback, you can see that the football does travel like that.\u003c/p\u003e\u003cp data-block-key=\"4jde2\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e So why does the nose of the football go from pointing upward to rotating downard when most things stay the same orientation as they move through the air? There are two key players involved: gravity and angular momentum. Ok, so what is angular momentum? First, it’ll help to understand momentum. You’re probably used to experiencing \u003ci\u003elinear\u003c/i\u003e momentum. Imagine you’re a passenger in a car traveling at 40 miles per hour and the driver suddenly breaks, but you continue moving forward. That’s what seatbelts are for.\u003c/p\u003e\u003cp data-block-key=\"7b3c1\"\u003e\u003cb\u003eSteve Lamoreaux:\u003c/b\u003e A body in motion tends to stay in motion unless acted on by a force, and that\u0026#x27;s conservation of momentum.\u003c/p\u003e\u003cp data-block-key=\"o1e3\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Then there is angular momentum, which is when an object with mass is spinning. You can see this property in action when an ice skater speeds up when they pull their arms in. In football, conservation of angular momentum is the reason why the ball changes orientation while it spins through the air. Let\u0026#x27;s compare a football spinning vertically on a flat surface to a spinning top.\u003c/p\u003e\u003cp data-block-key=\"c52dm\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e The top of the top will describe a circular orbit around a vertical axis. The vertical axis is set up by the force of gravity. Gravity is trying to pull the top over, but the top refuses to fall over. To conserve angular momentum, it processes in a circle.\u003c/p\u003e\u003cp data-block-key=\"6qpne\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e A football acts kind of like a top—a symmetrical top.\u003c/p\u003e\u003cp data-block-key=\"64kij\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e Now, the axis about which the ball rotates is not caused by gravity. In the case of the football, it\u0026#x27;s precessing around the onrushing force of air that the ball experiences.\u003c/p\u003e\u003cp data-block-key=\"a0op5\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The force of the air pushes on the ball, causing it to wobble around its spinning axis, and this wobble eventually pushes the nose down.\u003c/p\u003e\u003cp data-block-key=\"2slmd\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e Gravity absolutely acts on the football, but its effect is to cause the ball to go up and then come down in that curved parabolic trajectory.\u003c/p\u003e\u003cp data-block-key=\"dnuom\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Put them all together and you get that beautiful pass. But to gain the most amount of yards in the shortest amount of time, the quarterback needs to keep a lot of things in mind.\u003c/p\u003e\u003cp data-block-key=\"b3a04\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e The thing I look for in a quarterback is a lot of intelligence and understanding. After that it\u0026#x27;s accuracy with the arm, timing to get the ball out, and just awareness.\u003c/p\u003e\u003cp data-block-key=\"6vt9i\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e And the spin of the ball is crucial to getting it go the distance.\u003c/p\u003e\u003cp data-block-key=\"amip7\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e If you don\u0026#x27;t throw a spiral, that thing is going to flutter. We call those ducks. The ball starts to flutter, doesn\u0026#x27;t get velocity, doesn\u0026#x27;t get distance and those end up getting intercepted by the defenders.\u003c/p\u003e\u003cp data-block-key=\"7923n\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Here’s how they get that perfect spiral.\u003c/p\u003e\u003cp data-block-key=\"bs39c\"\u003e\u003cb\u003eBernard Davis:\u003c/b\u003e So your firm grip must come from these fingers. And the other last two in the back is also for guidance. And also try to have like a gap right here.\u003c/p\u003e\u003cp data-block-key=\"6ji2v\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e From that, it\u0026#x27;s all about where your arm is going and then the snap of your wrist.\u003c/p\u003e\u003cp data-block-key=\"cuo3u\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e And they have to release the ball quickly. In those seconds…\u003c/p\u003e\u003cp data-block-key=\"dlq3u\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e So once the ball is snapped, you know, the quarterback is focused on several different things. So we\u0026#x27;re catching the ball, we\u0026#x27;re also scanning what\u0026#x27;s going on in front of us. As we do that, we\u0026#x27;re backing up away from the line where we\u0026#x27;re going to throw the ball. So as we\u0026#x27;re doing that, we\u0026#x27;re actually flipping the ball to put the laces on our hand.\u003c/p\u003e\u003cp data-block-key=\"9m4v5\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Physics may be an integral part of football, but to players…\u003c/p\u003e\u003cp data-block-key=\"2hof8\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e It\u0026#x27;s all about timing and practice and repetition.\u003cbr/\u003e\u003c/p\u003e\n\n\n","passport_start":"2023-02-13T21:10:34+00:00","short_description":"\u003cp data-block-key=\"zu4f7\"\u003eThere are two key players involved: gravity and angular momentum.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"The Mystery and Physics of the Spiral Football Pass","slug":"mystery-and-physics-of-spiral-football-pass","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-mystery-and-physics-of-the-spiral-football-pass-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1676478593981]},{"_index":"content","_type":"doc","_id":"sfv-6571","_score":null,"_source":{"slug":"teen-calculates-mind-boggling-math-in-head","title":"This Teen Calculates Mind-Boggling Math in Her Head","topic":"physics","brand":"nova","content_type":"shortvideopage","length":190,"publish_date":"2022-12-14T18:40:48.878902+00:00","tags":["mental math","genius","game show","STEM","calculator","human calculator","mathematics","math genius","teenager","math","math problems","problem solving","abacus"],"external":false,"published":true,"hero_image":{"mime_type":"image/png","alt_text":"Apoorva Panidapu","src":"https://www.pbs.org/wgbh/nova/media/original_images/Screenshot_20230130_124126.png","renditions":[{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-300.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"54xuh\"\u003eApoorva Panidapu earned the moniker “the human calculator” for her math skills.\u003c/p\u003e\n\u003cp data-block-key=\"0ci43\"\u003ePanidapu executes complex problems with mental math using the abacus method of calculation, a technique that relies on an ancient tool.\u003c/p\u003e\n\u003cp data-block-key=\"cdcxc\"\u003e\u003cb\u003eThis Teen Calculates Mind-Boggling Math in Her Head\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"6su3k\"\u003ePublished December 14, 2022\u003c/p\u003e\u003cp data-block-key=\"5112q\"\u003e\u003c/p\u003e\u003cp data-block-key=\"679sh\"\u003e\u003cb\u003eApoorva Panidapu\u003c/b\u003e: So I was on a show called Genius Junior when I was 12 years old.\u003c/p\u003e\u003cp data-block-key=\"3d563\"\u003e\u003cb\u003eShow Host:\u003c/b\u003e 121 plus 13 squared times two -44 equals.\u003c/p\u003e\u003cp data-block-key=\"a7b7d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e 536.\u003c/p\u003e\u003cp data-block-key=\"240m8\"\u003e\u003cb\u003eShow Host:\u003c/b\u003e Correct.\u003c/p\u003e\u003cp data-block-key=\"fef1o\"\u003e\u003cb\u003eApoorva Panidapu\u003c/b\u003e: On that show, I did a bunch of computations in a round called the number-cruncher. I’m Apoorva Panidapu, I\u0026#x27;m 17, and some people call me the human calculator. I started my journey in math with something called abacus, which is an ancient computation method when I was five or six years old. It\u0026#x27;s just a different way of thinking about computation, adding, subtracting, all of the operations.\u003c/p\u003e\u003cp data-block-key=\"e9u7q\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e On this abacus, each column represents a different place value. And these beads are moved when counting, or to perform mathematical operations.\u003c/p\u003e\u003cp data-block-key=\"2v2c6\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e I don\u0026#x27;t use my physical abacus as often as I used to, just because I mostly do it in my head nowadays. The beauty of it was being able to push myself farther and farther, challenge my brain, but also be able to see these patterns. And that just snowballed into doing math competitions, learning as much as I could about it.\u003c/p\u003e\u003cp data-block-key=\"9rcfe\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e To put Apoorva’s mental math skills to the test. We\u0026#x27;ve come up with a problem that\u0026#x27;s fit for NOVA, and asked Apoorva to share her secrets to solving it. A rocket is traveling at a consistent velocity of 4,300 kilometers per hour. How many hours will it take to reach a planet? 2.35 million kilometers away.\u003c/p\u003e\u003cp data-block-key=\"1vv0d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e It\u0026#x27;s the same way you think about it in traditional division. But you start with this number, and you estimate how many groups of this can go into it first. And so I would go with five. You just keep subtracting it, but it happens in your head, four and then presumably six.\u003c/p\u003e\u003cp data-block-key=\"15it\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e I can\u0026#x27;t keep up with that, so what about multiplication? What is 34 times 76?\u003c/p\u003e\u003cp data-block-key=\"evb5d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e 34 times 76 is 2584.\u003c/p\u003e\u003cp data-block-key=\"2sb8f\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Wow.\u003c/p\u003e\u003cp data-block-key=\"13mfj\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e So the way I did it is kind of similar to how you did in school is I do the two-digit times this one digit first, and in my head I have it as 238, and then I do 34 times 6 and then that\u0026#x27;s 204. And then I sort of use the abacus in my head and that gives me 2584. But a nice trade secret: as you\u0026#x27;re calculating it, you can start saying the answer because you know, it starts with the 2 and then as you\u0026#x27;re adding, you\u0026#x27;re like, okay, the next one is 5, the next one is 8. I think you can\u0026#x27;t do any of STEM without the M. How do you interpret data? How do you interpret experiments and how do you interpret the world? Being good at math, it just means having confidence going into a problem. I\u0026#x27;m technically homeschooled, but I take classes at my local universities and it\u0026#x27;s a state and also online program with Johns Hopkins University. And then I also do like random online AP courses. Where I\u0026#x27;m going to go to school is to be determined because I\u0026#x27;m a senior doing college applications right now, but hopefully somewhere that I fit i\u003c/p\u003e\n\n\n","passport_start":"2022-12-14T15:41:24+00:00","short_description":"\u003cp data-block-key=\"54xuh\"\u003eApoorva Panidapu earned the moniker “the human calculator” for her math skills.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"This Teen Calculates Mind-Boggling Math in Her Head","slug":"teen-calculates-mind-boggling-math-in-head","page_type":"shortvideopage","canonical_image":{"mime_type":"image/png","alt_text":"Apoorva Panidapu","src":"https://www.pbs.org/wgbh/nova/media/original_images/Screenshot_20230130_124126.png","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-300.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2500.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1671043248878]},{"_index":"content","_type":"doc","_id":"sfv-6573","_score":null,"_source":{"slug":"scientists-make-breakthrough-in-nuclear-fusion","title":"Scientists Make Breakthrough in Nuclear Fusion","topic":"physics","brand":"nova","content_type":"shortvideopage","length":113,"publish_date":"2022-12-14T18:39:44.254657+00:00","tags":["atom","fusion","fusion power","star","star power","scientific breakthrough","lawrence livermore national laboratory","nuclear fusion","clean energy","star fusion","department of energy","hydrogen fusion","atoms"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/scientists-achieve-breakthrough-in-nuclear-fusion-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"6ypwu\"\u003eThe advancement could help pave the way for new energy sources.\u003c/p\u003e\n\u003cp data-block-key=\"gokl3\"\u003eFor the first time, lab-made fusion released more energy than it used to start the reaction, a feat that has eluded researchers for decades.\u003c/p\u003e\n\u003cp data-block-key=\"40bxw\"\u003e\u003cb\u003eScientists Make Breakthrough in Nuclear Fusion\u003cbr/\u003e\u003c/b\u003ePublished December 14, 2022\u003c/p\u003e\u003cp data-block-key=\"4afh2\"\u003e\u003c/p\u003e\u003cp data-block-key=\"enh6o\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Scientists made a major breakthrough in the field of nuclear fusion, one that could help pave the way to a nearly limitless source of clean energy. The announcement excited officials.\u003c/p\u003e\u003cp data-block-key=\"63vqt\"\u003e\u003cb\u003eJennifer M. Granholm:\u003c/b\u003e Simply put, this is one of the most impressive scientific feats of the 21st century. This is a BFD.\u003c/p\u003e\u003cp data-block-key=\"6ognf\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Fusion is the nuclear process that powers the sun and occurs when the nuclei of two atoms combine releasing energy. And for the first time lab made fusion released more energy than it took to start the reaction, a feat that has eluded researchers for decades.\u003c/p\u003e\u003cp data-block-key=\"8om61\"\u003e\u003cb\u003eMark Herrmann:\u003c/b\u003e That\u0026#x27;s never been done before in any fusion laboratory anywhere in the world, so it\u0026#x27;s super exciting.\u003c/p\u003e\u003cp data-block-key=\"bqoj4\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e To do it, scientists blasted 192 lasers at a pellet of fuel to fuze hydrogen atoms. Fusion could one day produce a massive amount of emissions free energy without the long lasting nuclear waste that fission in nuclear power plants produce and without the risk of nuclear meltdown. But they\u0026#x27;re still a ways off from getting energy on the grid.\u003c/p\u003e\u003cp data-block-key=\"3a8rs\"\u003e\u003cb\u003eKim Budil:\u003c/b\u003e This is one igniting capsule one time. And to realize commercial fusion energy, you have to do many things. You have to be able to produce many, many fusion ignition events per minute. And you have to have a robust system of drivers to enable that. So, you know, probably decades.\u003c/p\u003e\u003cp data-block-key=\"4v0rf\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Still, recent advances in the field using a variety of fusion techniques are bringing the possibility of fusion energy closer to becoming a reality.\u003c/p\u003e\u003cp data-block-key=\"2h0aa\"\u003e\u003cb\u003eKim Budil:\u003c/b\u003e Not six decades, I don\u0026#x27;t think. I think not five decades, which is what we used to say. I think it\u0026#x27;s moving into the foreground and probably, you know, with concerted effort and investment, a few decades of research on the underlying technologies could put us in a position to build a power plant.\u003c/p\u003e\n\n\n","passport_start":"2022-12-14T15:50:32+00:00","short_description":"\u003cp data-block-key=\"6ypwu\"\u003eThe advancement could help pave the way for new energy sources.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"Scientists Make Breakthrough in Nuclear Fusion","slug":"scientists-make-breakthrough-in-nuclear-fusion","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/scientists-achieve-breakthrough-in-nuclear-fusion-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1671043184254]},{"_index":"content","_type":"doc","_id":"article-6563","_score":null,"_source":{"slug":"math-teaching-resources-zero-to-infinity","title":"Teaching resources: How ancient cultures shaped mathematics","topic":"physics","brand":"education","content_type":"article","publish_date":"2022-12-01T21:33:00+00:00","external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"The hindu arabic numerals displayed on an ancient text","caption":{"html":"\u003cp\u003eThe numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH\u003c/p\u003e","plaintext":"The numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cdiv class=\"related\"\u003e\u003c/div\u003e\n\u003cp\u003eIn NOVA’s new documentary \u003ca href=\"https://www.pbs.org/wgbh/nova/video/zero-to-infinity/\"\u003eZero to Infinity\u003c/a\u003e, mathematician Talithia Williams takes viewers on a global journey to discover how the concepts of zero and infinity revolutionized mathematics across different cultures over thousands of years. Now, the \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova-zero-to-infinity/\"\u003eZero to Infinity collection on PBS LearningMedia\u003c/a\u003e features excerpts from the film contextualized with background readings, teaching tips, and discussion questions to help students understand the history of these fundamental concepts. For example, many of the numeral systems used by ancient cultures did not include the number zero. The earliest documented use of zero is believed to be in a manuscript from India dated to as early as the third or fourth century.\u003c/p\u003e\u003cp\u003eStudents also have the chance to learn about the work of Persian mathematician Muhammad ibn Mūsā al-Khwārizmī, who conducted his research out of the “House of Wisdom” (a.k.a. the Grand Library of Baghdad) more than a thousand years ago. In a book on arithmetic al-Khwārizmī wrote in about 825 CE, he explains the Hindu–Arabic numbers and how to perform addition, subtraction, multiplication, division, doubling, and halving as well as how to calculate with fractions.\u003c/p\u003e\n\u003cdiv class=\"pullquote\"\u003e\n\u003cp\u003eA good thing in [math] education would be to cut down the content a bit and savor these ideas.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e“A good thing in [math] education would be to cut down the content a bit and savor these ideas,” mathematician \u003ca href=\"https://www.youtube.com/watch?v=Gra6wqrxO-0\u0026amp;t=576s\"\u003eManjul Bhargava\u003c/a\u003e said during a Zero to Infinity live-streamed panel on the NOVA YouTube channel. “We just had a whole hour show on zero and infinity talking about the beauty of it. We never get to do that in school, and we should really appreciate these concepts.”\u003c/p\u003e\n\u003cp\u003eEugenia Cheng, another mathematician featured in the film\u003ci\u003e,\u003c/i\u003e wishes teachers had the chance to be more expansive with math curriculum, and focus on the wonder of math, as opposed to teaching content optimized for standardized test score performance.\u003c/p\u003e\u003cp\u003e“Most of the math we are going to learn in school we are not going to directly use,” Cheng said during the panel discussion. “It’s important that we learn to use our brain in a rigorous, systematic, and efficient way that enables us to take in different points of view and make connections between things.”\u003c/p\u003e\n\u003cfigure class=\"richtext-image full-width\"\u003e\n\u003cimg alt=\"A youtube conversation with Talithia Williams, Manjul Bhargava, and Eugenia Cheng\" class=\"richtext-image full-width\" src=\"https://www.pbs.org/wgbh/nova/media/images/ZTI_livestream.width-990.png\"/\u003e\n\u003cfigcaption\u003e\u003cp\u003eMathematicians Talithia Williams, Manjul Bhargava, and Eugenia Cheng answer questions about the concepts of zero and infinity during a live conversation on Youtube following the premiere of NOVA's latest documentary, Zero to Infinity.\u003c/p\u003e\n\u003c/figcaption\u003e\n\u003c/figure\u003e\n\u003cp\u003eWhether students are curious about where today’s number system and basic math functions came from, or want to solve real-world problems to better understand \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-number-quantity/\"\u003enumber and quantity\u003c/a\u003e, \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-geometry/\"\u003egeometry\u003c/a\u003e,\u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-algebra/\"\u003e algebra\u003c/a\u003e, or \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-statistics/\"\u003estatistics\u003c/a\u003e concepts, this collection of math resources from NOVA can help bolster learning for grades 6-8!\u003c/p\u003e\n\u003cdiv class=\"ad\"\u003e\u003c/div\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-hinduarabicnumerals/hinduarabic-numerals-and-algebra-zero-to-infinity/\"\u003e\u003cb\u003eHindu-Arabic Numerals and Algebra | Zero to Infinity (Grades: 9-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eLearn where today’s widely used number system and basic math functions came from, and how the decimal system was developed. The set of ten numerals—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—that you have used all your life make up the Hindu-Arabic system, also known as the decimal system or base-ten system. It is a place value (or “positional”) system, meaning that the value of a numeral depends on its position. The values increase by powers of ten. For example, in the number 3,286, “6” is in the ones place while “3” is in the thousands place; the value of each numeral is its value multiplied by the value of the place—the “3” in the number represents 3,000.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-historyofzero/the-history-of-zero-zero-to-infinity/\"\u003e\u003cb\u003eThe History of Zero | Zero to Infinity (Grades: 6-8)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eAlthough it’s easy to take the concept of zero for granted, this digit representing “none” actually had to be invented. Learn about when and where the zero we use today originated.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-pizzacirclearea/calculating-the-area-of-a-circle-using-pizza-slices-zero-to-infinity/\"\u003e\u003cb\u003eCalculating the Area of a Circle Using Pizza Slices | Zero to Infinity (Grades: 6-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eFinding the area of a circle is easy with a simple formula involving pi. But how could people have done it before they knew about pi? Learn how the concept of infinity can help convert a circular pizza into a rectangle, making it much easier to measure. Use this resource to help students reason abstractly and construct an argument about the formula for the area of a circle.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-calculusparadoxeslimits/zenos-paradoxes-and-limits-in-calculus-zero-to-infinity/\"\u003e\u003cb\u003eZeno’s Paradoxes and Limits in Calculus | Zero to Infinity (Grades: 9-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eIn the fifth century BCE, the Greek philosopher Zeno of Elea thought deeply about time and motion. Zeno is most famous for describing several paradoxes where if one assumes space and time are infinitely divisible, then it follows that motion is an illusion. More than a thousand years after Zeno’s death, a new branch of mathematics called calculus helped make sense of his paradoxes. Use this resource to provide opportunities for students to calculate how fast an object is moving at a particular instant using limits in calculus.\u003c/p\u003e\n\u003cdiv class=\"newsletter\"\u003e\u003c/div\u003e","author":["kara-norton-"],"short_description":"\u003cp data-block-key=\"waalc\"\u003eFrom the ancient origins of zero to the paradox of motion, NOVA’s teaching resources immerse students in the wonder of math.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"Teaching resources: How ancient cultures shaped mathematics","slug":"math-teaching-resources-zero-to-infinity","page_type":"article","canonical_image":{"mime_type":"image/jpeg","alt_text":"The hindu arabic numerals displayed on an ancient text","caption":{"html":"\u003cp\u003eThe numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH\u003c/p\u003e","plaintext":"The numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1669930380000]},{"_index":"content","_type":"doc","_id":"article-6561","_score":null,"_source":{"slug":"math-thought-experiment-zero-infinity","title":"4 mind-bending math experiments that explain infinity","topic":"physics","brand":"next","content_type":"article","publish_date":"2022-11-29T16:55:12.595930+00:00","tags":["geometry","infinity","math","trigonometry","set theory","algebra","thought experiment","calculus"],"dci":["mathematical-sciences"],"external":false,"published":true,"hero_image":{"mime_type":"image/png","alt_text":"On a black background, a row of 6 red die lines up with a row of 6 red shoes, with white lines connecting them","caption":{"html":"\u003cp\u003eA set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA\u003c/p\u003e","plaintext":"A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/Set_theory_hero.png","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-300.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cdiv class=\"related\"\u003e\u003c/div\u003e\n\u003cp\u003eIt can be easy to take math for granted. But the field has evolved over millennia, and concepts that seem obvious today had to be invented. Although zero is the beginning of counting, it arrived late to the math party. But not as late as its counterpart, infinity. Four thought experiments featured in NOVA’s “\u003ca href=\"https://www.pbs.org/wgbh/nova/video/zero-to-infinity/\"\u003eZero to Infinity\u003c/a\u003e” illustrate how people used the world around them to explore these revolutionary concepts.\u003c/p\u003e\n\u003ch3\u003e\u003cb\u003eHow infinity can help determine the area of a pizza (without pi) \u003c/b\u003e\u003c/h3\u003e\u003cp\u003ePizza is an interesting dish–a circle cut into triangles and served in a square box—an elusive mystery of early mathematics. Not the serving of the pizza, but the circle itself. See, squares and rectangles have straight lines, so it’s easy to determine their area. A circle, on the other hand, left ancient scholars scratching their heads. One solution: infinity.\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/cmd4wrtqDNaP6ev8jLbXJw==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eHilbert’s Hotel: Is there room for one more at a hotel with infinite rooms?\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eInfinity can be a tough concept to grasp. But mathematician David Hilbert came up with a more concrete way to think about it: A hotel with an infinite number of rooms–all occupied. What happens when one more guest shows up? What about an infinite number of guests, all evacuated from another nearby “Hilbert’s hotel” that caught on fire? Is there room for everyone?\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/kxjvkssttL0dWY49v-Ch6w==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cdiv class=\"ad\"\u003e\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eZeno’s Paradox: Infinity turns a speeding arrow into an illusion (25:44 - 30:24)\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eThe Greek philosopher Zeno of Elea came up with a paradox that questioned the very idea of motion. Suppose you shoot an arrow and try to calculate its speed. You need to divide the distance traveled by the amount of time elapsed. But supposing that instead of moving, the arrow is actually at rest for an infinity of instants, then you would be dividing by zero–which is against the rules of mathematics.\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/OP-VBloee-XyDYXck2GEMA==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eCantor’s Theorem: Some infinities are bigger than others (44:06 - 51:00)\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eGerman mathematician Georg Cantor helped us think about how big infinity actually is. He created a concept called “set theory,” in which you have a defined collection, or \"set,\" of things, and if they match up one-to-one with another set of things, then both sets are the same size. But let’s say you take an infinite set of counting numbers (1,2,3…) and match it up to an infinite set of even numbers. Which one is bigger? It turns out they are exactly the same size. Here’s why:\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/OP-VBloee-XyDYXck2GEMA==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cdiv class=\"newsletter\"\u003e\u003c/div\u003e","author":["attabey-rodriguez-benitez"],"short_description":"\u003cp data-block-key=\"03b0f\"\u003eCan one infinity be bigger than another?\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"4 mind-bending math experiments that explain infinity","slug":"math-thought-experiment-zero-infinity","page_type":"article","canonical_image":{"mime_type":"image/png","alt_text":"On a black background, a row of 6 red die lines up with a row of 6 red shoes, with white lines connecting them","caption":{"html":"\u003cp\u003eA set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA\u003c/p\u003e","plaintext":"A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/Set_theory_hero.png","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-300.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2500.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1669740912595]}]}},"split_search_results":{"first":[{"_index":"content","_type":"doc","_id":"sfv-6815","_score":null,"_source":{"slug":"one-of-the-greatest-meetings-of-the-minds-in-history","title":"One of the Greatest Meetings of the Minds in History","topic":"physics","brand":"nova","content_type":"shortvideopage","length":148,"publish_date":"2024-08-27T23:54:56.958694+00:00","tags":["1927 Solvay Conference","quantum","Wolfgang Pauli","Heisenberg","Quantum entanglement,","einstein","quantum entanglement","quantum mechanics"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/one-of-the-greatest-meetings-of-the-minds-in-history-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"47aso\"\u003eThese scientists were the pioneers of quantum mechanics.\u003c/p\u003e\n\u003cp data-block-key=\"7md9n\"\u003eThe theory of quantum mechanics presented at the meeting said that a particle like an electron isn’t physically real until it’s observed, measured by an instrument that can detect it. Before it’s detected, instead of being a solid particle, an electron is just a fuzzy wave, a wave of probability.\u003c/p\u003e\n\u003cp data-block-key=\"du910\"\u003e\u003cb\u003eOne of the Greatest Meetings of the Minds in History\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"fqeho\"\u003ePublished: August 27, 2024\u003c/p\u003e\u003cp data-block-key=\"5m8hn\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e It was the nature of fundamental particles which make up the world we see around us that Einstein had come to Brussels to discuss, and it was here that Einstein entered into a heated debate that would lead to the discovery of quantum entanglement, a concept that would trouble him for the rest of his life.\u003c/p\u003e\u003cp data-block-key=\"43mcn\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e This is the original Solvay Institute building, and this is the place back in October 1927 where the fifth Solvay Conference was held. This amazing week-long series of discussions on really what the world is made of, on the nature of matter and the new quantum theory, and these steps are the very steps on which this famous group photograph was taken. It\u0026#x27;s a collection of some of the most brilliant people in the world.\u003c/p\u003e\u003cp data-block-key=\"a9d9n\"\u003eHere in the front row, we see Albert Einstein and the great Marie Curie and Max Planck. In the back row standing, the dapper Erwin Schrödinger, and these brash 20-year-olds or mid-20s, Werner Heisenberg and Wolfgang Pauli.\u003c/p\u003e\u003cp data-block-key=\"cknj8\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e These scientists were the pioneers of quantum mechanics.\u003c/p\u003e\u003cp data-block-key=\"7em10\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e I had a huge version of this photograph up on the wall. It was a poster in my college dorm room. My roommates had their favorite bands, and I had the 1927 Solvay Conference, which says a lot.\u003c/p\u003e\u003cp data-block-key=\"esp0s\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e This was one of the greatest meetings of minds in history. More than half were or would become Nobel Prize winners. Their experiments were showing that deep inside matter tiny particles like atoms and their orbiting electrons were not solid little spheres, they seemed fuzzy and undefined.\u003c/p\u003e\u003cp data-block-key=\"61slt\"\u003e\u003cb\u003eDavid Kaiser:\u003c/b\u003e So this group here, these were the folks who had just been plumbing deeper and deeper and deeper to find what they hoped would be a bedrock of what the world is made of, and to their surprise they found things less and less solid as they dug in. This world was not tiny little bricks that got smaller and smaller. At some point, the bricks gave way to this mush, and what looked like solidity, solidness, in fact became very confusing and kind of a whole new way of thinking about nature.\u003c/p\u003e\n\n\n","passport_start":"2024-08-27T22:21:55+00:00","short_description":"\u003cp data-block-key=\"47aso\"\u003eThese scientists were the pioneers of quantum mechanics.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"One of the Greatest Meetings of the Minds in History","slug":"one-of-the-greatest-meetings-of-the-minds-in-history","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/one-of-the-greatest-meetings-of-the-minds-in-history-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-h.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/one-of-the-greatest-meetings-of-the-minds-in-.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1724802896958]},{"_index":"content","_type":"doc","_id":"sfv-6814","_score":null,"_source":{"slug":"the-hippy-days-of-quantum-physics","title":"The “Hippy Days” of Quantum Physics","topic":"physics","brand":"nova","content_type":"shortvideopage","length":103,"publish_date":"2024-08-27T04:24:03.009203+00:00","tags":["70s science","einstein's quantum riddle","hippy science","Fundamental Fysiks Group","1970s","70s","quantum","quantum physics","einstein"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-hippy-days-of-quantum-physics-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"6mu2u\"\u003eHow a group of free-thinking physicists in the 1970s helped shape quantum physics.\u003c/p\u003e\n\u003cp data-block-key=\"jlnbl\"\u003eIn seeing quantum entanglement as central to physics, The Fundamental Fysiks Group were decades ahead of their time.\u003c/p\u003e\n\u003cp data-block-key=\"ujdqk\"\u003e\u003cb\u003eThe “Hippy Days” of Quantum Physics\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"38qia\"\u003ePublished: August 27, 2024\u003c/p\u003e\u003cp data-block-key=\"6i67u\"\u003e\u003cb\u003eSpeaker 1:\u003c/b\u003e They call themselves the Fundamental Fysics Group, they spelled Fysics with an F. Some members would experiment with psychedelic drugs. I mean, they were in the flow of the hippie scene, and that group was just mesmerized by the question of entanglement.\u003c/p\u003e\u003cp data-block-key=\"48cms\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e The idea was just to discuss fringe subjects with an open mind, and I thought of, \u0026quot;Sure, that\u0026#x27;s kind of what I do.\u0026quot; They were doing their best to link eastern mysticism with quantum entanglement. They sold a lot of popular textbooks. There were a lot of followers.\u003c/p\u003e\u003cp data-block-key=\"6rldk\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Their books became bestsellers like The Tao of Physics, which highlighted that Eastern philosophy and quantum entanglement both described the deep connectedness of things in the universe.\u003c/p\u003e\u003cp data-block-key=\"eesa\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e It was the great cosmic oneness.\u003c/p\u003e\u003cp data-block-key=\"jgf6\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The group held meetings at the iconic Esalen Institute.\u003c/p\u003e\u003cp data-block-key=\"dq2bl\"\u003e\u003cb\u003eSpeaker 2:\u003c/b\u003e It was a marvelous, beautiful place where they would discuss all of these ideas. It was right on the Pacific coast with the overflow from the hot tubs cascading down the cliffs into the Pacific Ocean. To my knowledge, no useful connections to Eastern mysticism were ever discovered by the group, but it was fun.\u003c/p\u003e\u003cp data-block-key=\"d1ml8\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The Fundamental Fysics group may not have uncovered the secrets of cosmic oneness, but in seeing entanglement as central to physics, they were decades ahead of their time.\u003c/p\u003e\n\n\n","passport_start":"2024-08-27T01:00:12+00:00","short_description":"\u003cp data-block-key=\"6mu2u\"\u003eHow a group of free-thinking physicists in the 1970s helped shape quantum physics.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"The “Hippy Days” of Quantum Physics","slug":"the-hippy-days-of-quantum-physics","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-hippy-days-of-quantum-physics-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-hippy-days-of-quantum-physics-hero.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1724732643009]}],"second":[{"_index":"content","_type":"doc","_id":"sfv-6593","_score":null,"_source":{"slug":"mystery-and-physics-of-spiral-football-pass","title":"The Mystery and Physics of the Spiral Football Pass","topic":"physics","brand":"nova","content_type":"shortvideopage","length":223,"publish_date":"2023-02-15T16:29:53.981920+00:00","tags":["football","physics","sports","mystery","physics in sports","spiral pass","spiral football pass"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-mystery-and-physics-of-the-spiral-football-pass-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"zu4f7\"\u003eThere are two key players involved: gravity and angular momentum.\u003c/p\u003e\n\u003cp data-block-key=\"6otjm\"\u003eThe way the spiral football pass travels through the air baffled physicists for years.\u003c/p\u003e\n\u003cp data-block-key=\"zgifh\"\u003e\u003cb\u003eThe Mystery and Physics of the Spiral Football Pass\u003cbr/\u003e\u003c/b\u003ePublished February 15, 2023\u003cbr/\u003e\u003c/p\u003e\u003cp data-block-key=\"eibhd\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The perfect football pass, a thing of beauty—and bewilderment. The way the football travels mid-air baffled physicists for years.\u003c/p\u003e\u003cp data-block-key=\"866nm\"\u003e\u003cb\u003eSteve Lamoreaux\u003c/b\u003e: If you\u0026#x27;re in the physicist\u0026#x27;s world, you expect a football to travel like this and come down. When you watch a long pass from a talented quarterback, you can see that the football does travel like that.\u003c/p\u003e\u003cp data-block-key=\"4jde2\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e So why does the nose of the football go from pointing upward to rotating downard when most things stay the same orientation as they move through the air? There are two key players involved: gravity and angular momentum. Ok, so what is angular momentum? First, it’ll help to understand momentum. You’re probably used to experiencing \u003ci\u003elinear\u003c/i\u003e momentum. Imagine you’re a passenger in a car traveling at 40 miles per hour and the driver suddenly breaks, but you continue moving forward. That’s what seatbelts are for.\u003c/p\u003e\u003cp data-block-key=\"7b3c1\"\u003e\u003cb\u003eSteve Lamoreaux:\u003c/b\u003e A body in motion tends to stay in motion unless acted on by a force, and that\u0026#x27;s conservation of momentum.\u003c/p\u003e\u003cp data-block-key=\"o1e3\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Then there is angular momentum, which is when an object with mass is spinning. You can see this property in action when an ice skater speeds up when they pull their arms in. In football, conservation of angular momentum is the reason why the ball changes orientation while it spins through the air. Let\u0026#x27;s compare a football spinning vertically on a flat surface to a spinning top.\u003c/p\u003e\u003cp data-block-key=\"c52dm\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e The top of the top will describe a circular orbit around a vertical axis. The vertical axis is set up by the force of gravity. Gravity is trying to pull the top over, but the top refuses to fall over. To conserve angular momentum, it processes in a circle.\u003c/p\u003e\u003cp data-block-key=\"6qpne\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e A football acts kind of like a top—a symmetrical top.\u003c/p\u003e\u003cp data-block-key=\"64kij\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e Now, the axis about which the ball rotates is not caused by gravity. In the case of the football, it\u0026#x27;s precessing around the onrushing force of air that the ball experiences.\u003c/p\u003e\u003cp data-block-key=\"a0op5\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e The force of the air pushes on the ball, causing it to wobble around its spinning axis, and this wobble eventually pushes the nose down.\u003c/p\u003e\u003cp data-block-key=\"2slmd\"\u003e\u003cb\u003eTim Gay:\u003c/b\u003e Gravity absolutely acts on the football, but its effect is to cause the ball to go up and then come down in that curved parabolic trajectory.\u003c/p\u003e\u003cp data-block-key=\"dnuom\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Put them all together and you get that beautiful pass. But to gain the most amount of yards in the shortest amount of time, the quarterback needs to keep a lot of things in mind.\u003c/p\u003e\u003cp data-block-key=\"b3a04\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e The thing I look for in a quarterback is a lot of intelligence and understanding. After that it\u0026#x27;s accuracy with the arm, timing to get the ball out, and just awareness.\u003c/p\u003e\u003cp data-block-key=\"6vt9i\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e And the spin of the ball is crucial to getting it go the distance.\u003c/p\u003e\u003cp data-block-key=\"amip7\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e If you don\u0026#x27;t throw a spiral, that thing is going to flutter. We call those ducks. The ball starts to flutter, doesn\u0026#x27;t get velocity, doesn\u0026#x27;t get distance and those end up getting intercepted by the defenders.\u003c/p\u003e\u003cp data-block-key=\"7923n\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Here’s how they get that perfect spiral.\u003c/p\u003e\u003cp data-block-key=\"bs39c\"\u003e\u003cb\u003eBernard Davis:\u003c/b\u003e So your firm grip must come from these fingers. And the other last two in the back is also for guidance. And also try to have like a gap right here.\u003c/p\u003e\u003cp data-block-key=\"6ji2v\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e From that, it\u0026#x27;s all about where your arm is going and then the snap of your wrist.\u003c/p\u003e\u003cp data-block-key=\"cuo3u\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e And they have to release the ball quickly. In those seconds…\u003c/p\u003e\u003cp data-block-key=\"dlq3u\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e So once the ball is snapped, you know, the quarterback is focused on several different things. So we\u0026#x27;re catching the ball, we\u0026#x27;re also scanning what\u0026#x27;s going on in front of us. As we do that, we\u0026#x27;re backing up away from the line where we\u0026#x27;re going to throw the ball. So as we\u0026#x27;re doing that, we\u0026#x27;re actually flipping the ball to put the laces on our hand.\u003c/p\u003e\u003cp data-block-key=\"9m4v5\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Physics may be an integral part of football, but to players…\u003c/p\u003e\u003cp data-block-key=\"2hof8\"\u003e\u003cb\u003eShane Cheltenham:\u003c/b\u003e It\u0026#x27;s all about timing and practice and repetition.\u003cbr/\u003e\u003c/p\u003e\n\n\n","passport_start":"2023-02-13T21:10:34+00:00","short_description":"\u003cp data-block-key=\"zu4f7\"\u003eThere are two key players involved: gravity and angular momentum.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"The Mystery and Physics of the Spiral Football Pass","slug":"mystery-and-physics-of-spiral-football-pass","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/the-mystery-and-physics-of-the-spiral-football-pass-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-football.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/the-mystery-and-physics-of-the-spiral-footbal.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1676478593981]},{"_index":"content","_type":"doc","_id":"sfv-6571","_score":null,"_source":{"slug":"teen-calculates-mind-boggling-math-in-head","title":"This Teen Calculates Mind-Boggling Math in Her Head","topic":"physics","brand":"nova","content_type":"shortvideopage","length":190,"publish_date":"2022-12-14T18:40:48.878902+00:00","tags":["mental math","genius","game show","STEM","calculator","human calculator","mathematics","math genius","teenager","math","math problems","problem solving","abacus"],"external":false,"published":true,"hero_image":{"mime_type":"image/png","alt_text":"Apoorva Panidapu","src":"https://www.pbs.org/wgbh/nova/media/original_images/Screenshot_20230130_124126.png","renditions":[{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-300.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"54xuh\"\u003eApoorva Panidapu earned the moniker “the human calculator” for her math skills.\u003c/p\u003e\n\u003cp data-block-key=\"0ci43\"\u003ePanidapu executes complex problems with mental math using the abacus method of calculation, a technique that relies on an ancient tool.\u003c/p\u003e\n\u003cp data-block-key=\"cdcxc\"\u003e\u003cb\u003eThis Teen Calculates Mind-Boggling Math in Her Head\u003c/b\u003e\u003c/p\u003e\u003cp data-block-key=\"6su3k\"\u003ePublished December 14, 2022\u003c/p\u003e\u003cp data-block-key=\"5112q\"\u003e\u003c/p\u003e\u003cp data-block-key=\"679sh\"\u003e\u003cb\u003eApoorva Panidapu\u003c/b\u003e: So I was on a show called Genius Junior when I was 12 years old.\u003c/p\u003e\u003cp data-block-key=\"3d563\"\u003e\u003cb\u003eShow Host:\u003c/b\u003e 121 plus 13 squared times two -44 equals.\u003c/p\u003e\u003cp data-block-key=\"a7b7d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e 536.\u003c/p\u003e\u003cp data-block-key=\"240m8\"\u003e\u003cb\u003eShow Host:\u003c/b\u003e Correct.\u003c/p\u003e\u003cp data-block-key=\"fef1o\"\u003e\u003cb\u003eApoorva Panidapu\u003c/b\u003e: On that show, I did a bunch of computations in a round called the number-cruncher. I’m Apoorva Panidapu, I\u0026#x27;m 17, and some people call me the human calculator. I started my journey in math with something called abacus, which is an ancient computation method when I was five or six years old. It\u0026#x27;s just a different way of thinking about computation, adding, subtracting, all of the operations.\u003c/p\u003e\u003cp data-block-key=\"e9u7q\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e On this abacus, each column represents a different place value. And these beads are moved when counting, or to perform mathematical operations.\u003c/p\u003e\u003cp data-block-key=\"2v2c6\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e I don\u0026#x27;t use my physical abacus as often as I used to, just because I mostly do it in my head nowadays. The beauty of it was being able to push myself farther and farther, challenge my brain, but also be able to see these patterns. And that just snowballed into doing math competitions, learning as much as I could about it.\u003c/p\u003e\u003cp data-block-key=\"9rcfe\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e To put Apoorva’s mental math skills to the test. We\u0026#x27;ve come up with a problem that\u0026#x27;s fit for NOVA, and asked Apoorva to share her secrets to solving it. A rocket is traveling at a consistent velocity of 4,300 kilometers per hour. How many hours will it take to reach a planet? 2.35 million kilometers away.\u003c/p\u003e\u003cp data-block-key=\"1vv0d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e It\u0026#x27;s the same way you think about it in traditional division. But you start with this number, and you estimate how many groups of this can go into it first. And so I would go with five. You just keep subtracting it, but it happens in your head, four and then presumably six.\u003c/p\u003e\u003cp data-block-key=\"15it\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e I can\u0026#x27;t keep up with that, so what about multiplication? What is 34 times 76?\u003c/p\u003e\u003cp data-block-key=\"evb5d\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e 34 times 76 is 2584.\u003c/p\u003e\u003cp data-block-key=\"2sb8f\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Wow.\u003c/p\u003e\u003cp data-block-key=\"13mfj\"\u003e\u003cb\u003eApoorva Panidapu:\u003c/b\u003e So the way I did it is kind of similar to how you did in school is I do the two-digit times this one digit first, and in my head I have it as 238, and then I do 34 times 6 and then that\u0026#x27;s 204. And then I sort of use the abacus in my head and that gives me 2584. But a nice trade secret: as you\u0026#x27;re calculating it, you can start saying the answer because you know, it starts with the 2 and then as you\u0026#x27;re adding, you\u0026#x27;re like, okay, the next one is 5, the next one is 8. I think you can\u0026#x27;t do any of STEM without the M. How do you interpret data? How do you interpret experiments and how do you interpret the world? Being good at math, it just means having confidence going into a problem. I\u0026#x27;m technically homeschooled, but I take classes at my local universities and it\u0026#x27;s a state and also online program with Johns Hopkins University. And then I also do like random online AP courses. Where I\u0026#x27;m going to go to school is to be determined because I\u0026#x27;m a senior doing college applications right now, but hopefully somewhere that I fit i\u003c/p\u003e\n\n\n","passport_start":"2022-12-14T15:41:24+00:00","short_description":"\u003cp data-block-key=\"54xuh\"\u003eApoorva Panidapu earned the moniker “the human calculator” for her math skills.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"This Teen Calculates Mind-Boggling Math in Her Head","slug":"teen-calculates-mind-boggling-math-in-head","page_type":"shortvideopage","canonical_image":{"mime_type":"image/png","alt_text":"Apoorva Panidapu","src":"https://www.pbs.org/wgbh/nova/media/original_images/Screenshot_20230130_124126.png","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-300.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1664,"height":936,"src":"https://www.pbs.org/wgbh/nova/media/images/Screenshot_20230130_124126.width-2500.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1671043248878]},{"_index":"content","_type":"doc","_id":"sfv-6573","_score":null,"_source":{"slug":"scientists-make-breakthrough-in-nuclear-fusion","title":"Scientists Make Breakthrough in Nuclear Fusion","topic":"physics","brand":"nova","content_type":"shortvideopage","length":113,"publish_date":"2022-12-14T18:39:44.254657+00:00","tags":["atom","fusion","fusion power","star","star power","scientific breakthrough","lawrence livermore national laboratory","nuclear fusion","clean energy","star fusion","department of energy","hydrogen fusion","atoms"],"external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/scientists-achieve-breakthrough-in-nuclear-fusion-hero.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cp data-block-key=\"6ypwu\"\u003eThe advancement could help pave the way for new energy sources.\u003c/p\u003e\n\u003cp data-block-key=\"gokl3\"\u003eFor the first time, lab-made fusion released more energy than it used to start the reaction, a feat that has eluded researchers for decades.\u003c/p\u003e\n\u003cp data-block-key=\"40bxw\"\u003e\u003cb\u003eScientists Make Breakthrough in Nuclear Fusion\u003cbr/\u003e\u003c/b\u003ePublished December 14, 2022\u003c/p\u003e\u003cp data-block-key=\"4afh2\"\u003e\u003c/p\u003e\u003cp data-block-key=\"enh6o\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Scientists made a major breakthrough in the field of nuclear fusion, one that could help pave the way to a nearly limitless source of clean energy. The announcement excited officials.\u003c/p\u003e\u003cp data-block-key=\"63vqt\"\u003e\u003cb\u003eJennifer M. Granholm:\u003c/b\u003e Simply put, this is one of the most impressive scientific feats of the 21st century. This is a BFD.\u003c/p\u003e\u003cp data-block-key=\"6ognf\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Fusion is the nuclear process that powers the sun and occurs when the nuclei of two atoms combine releasing energy. And for the first time lab made fusion released more energy than it took to start the reaction, a feat that has eluded researchers for decades.\u003c/p\u003e\u003cp data-block-key=\"8om61\"\u003e\u003cb\u003eMark Herrmann:\u003c/b\u003e That\u0026#x27;s never been done before in any fusion laboratory anywhere in the world, so it\u0026#x27;s super exciting.\u003c/p\u003e\u003cp data-block-key=\"bqoj4\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e To do it, scientists blasted 192 lasers at a pellet of fuel to fuze hydrogen atoms. Fusion could one day produce a massive amount of emissions free energy without the long lasting nuclear waste that fission in nuclear power plants produce and without the risk of nuclear meltdown. But they\u0026#x27;re still a ways off from getting energy on the grid.\u003c/p\u003e\u003cp data-block-key=\"3a8rs\"\u003e\u003cb\u003eKim Budil:\u003c/b\u003e This is one igniting capsule one time. And to realize commercial fusion energy, you have to do many things. You have to be able to produce many, many fusion ignition events per minute. And you have to have a robust system of drivers to enable that. So, you know, probably decades.\u003c/p\u003e\u003cp data-block-key=\"4v0rf\"\u003e\u003cb\u003eNarrator:\u003c/b\u003e Still, recent advances in the field using a variety of fusion techniques are bringing the possibility of fusion energy closer to becoming a reality.\u003c/p\u003e\u003cp data-block-key=\"2h0aa\"\u003e\u003cb\u003eKim Budil:\u003c/b\u003e Not six decades, I don\u0026#x27;t think. I think not five decades, which is what we used to say. I think it\u0026#x27;s moving into the foreground and probably, you know, with concerted effort and investment, a few decades of research on the underlying technologies could put us in a position to build a power plant.\u003c/p\u003e\n\n\n","passport_start":"2022-12-14T15:50:32+00:00","short_description":"\u003cp data-block-key=\"6ypwu\"\u003eThe advancement could help pave the way for new energy sources.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"Scientists Make Breakthrough in Nuclear Fusion","slug":"scientists-make-breakthrough-in-nuclear-fusion","page_type":"shortvideopage","canonical_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/scientists-achieve-breakthrough-in-nuclear-fusion-hero.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fus.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/scientists-achieve-breakthrough-in-nuclear-fu.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1671043184254]},{"_index":"content","_type":"doc","_id":"article-6563","_score":null,"_source":{"slug":"math-teaching-resources-zero-to-infinity","title":"Teaching resources: How ancient cultures shaped mathematics","topic":"physics","brand":"education","content_type":"article","publish_date":"2022-12-01T21:33:00+00:00","external":false,"published":true,"hero_image":{"mime_type":"image/jpeg","alt_text":"The hindu arabic numerals displayed on an ancient text","caption":{"html":"\u003cp\u003eThe numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH\u003c/p\u003e","plaintext":"The numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cdiv class=\"related\"\u003e\u003c/div\u003e\n\u003cp\u003eIn NOVA’s new documentary \u003ca href=\"https://www.pbs.org/wgbh/nova/video/zero-to-infinity/\"\u003eZero to Infinity\u003c/a\u003e, mathematician Talithia Williams takes viewers on a global journey to discover how the concepts of zero and infinity revolutionized mathematics across different cultures over thousands of years. Now, the \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova-zero-to-infinity/\"\u003eZero to Infinity collection on PBS LearningMedia\u003c/a\u003e features excerpts from the film contextualized with background readings, teaching tips, and discussion questions to help students understand the history of these fundamental concepts. For example, many of the numeral systems used by ancient cultures did not include the number zero. The earliest documented use of zero is believed to be in a manuscript from India dated to as early as the third or fourth century.\u003c/p\u003e\u003cp\u003eStudents also have the chance to learn about the work of Persian mathematician Muhammad ibn Mūsā al-Khwārizmī, who conducted his research out of the “House of Wisdom” (a.k.a. the Grand Library of Baghdad) more than a thousand years ago. In a book on arithmetic al-Khwārizmī wrote in about 825 CE, he explains the Hindu–Arabic numbers and how to perform addition, subtraction, multiplication, division, doubling, and halving as well as how to calculate with fractions.\u003c/p\u003e\n\u003cdiv class=\"pullquote\"\u003e\n\u003cp\u003eA good thing in [math] education would be to cut down the content a bit and savor these ideas.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e“A good thing in [math] education would be to cut down the content a bit and savor these ideas,” mathematician \u003ca href=\"https://www.youtube.com/watch?v=Gra6wqrxO-0\u0026amp;t=576s\"\u003eManjul Bhargava\u003c/a\u003e said during a Zero to Infinity live-streamed panel on the NOVA YouTube channel. “We just had a whole hour show on zero and infinity talking about the beauty of it. We never get to do that in school, and we should really appreciate these concepts.”\u003c/p\u003e\n\u003cp\u003eEugenia Cheng, another mathematician featured in the film\u003ci\u003e,\u003c/i\u003e wishes teachers had the chance to be more expansive with math curriculum, and focus on the wonder of math, as opposed to teaching content optimized for standardized test score performance.\u003c/p\u003e\u003cp\u003e“Most of the math we are going to learn in school we are not going to directly use,” Cheng said during the panel discussion. “It’s important that we learn to use our brain in a rigorous, systematic, and efficient way that enables us to take in different points of view and make connections between things.”\u003c/p\u003e\n\u003cfigure class=\"richtext-image full-width\"\u003e\n\u003cimg alt=\"A youtube conversation with Talithia Williams, Manjul Bhargava, and Eugenia Cheng\" class=\"richtext-image full-width\" src=\"https://www.pbs.org/wgbh/nova/media/images/ZTI_livestream.width-990.png\"/\u003e\n\u003cfigcaption\u003e\u003cp\u003eMathematicians Talithia Williams, Manjul Bhargava, and Eugenia Cheng answer questions about the concepts of zero and infinity during a live conversation on Youtube following the premiere of NOVA's latest documentary, Zero to Infinity.\u003c/p\u003e\n\u003c/figcaption\u003e\n\u003c/figure\u003e\n\u003cp\u003eWhether students are curious about where today’s number system and basic math functions came from, or want to solve real-world problems to better understand \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-number-quantity/\"\u003enumber and quantity\u003c/a\u003e, \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-geometry/\"\u003egeometry\u003c/a\u003e,\u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-algebra/\"\u003e algebra\u003c/a\u003e, or \u003ca href=\"https://ny.pbslearningmedia.org/collection/nova/t/mathematical-sciences/nova-statistics/\"\u003estatistics\u003c/a\u003e concepts, this collection of math resources from NOVA can help bolster learning for grades 6-8!\u003c/p\u003e\n\u003cdiv class=\"ad\"\u003e\u003c/div\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-hinduarabicnumerals/hinduarabic-numerals-and-algebra-zero-to-infinity/\"\u003e\u003cb\u003eHindu-Arabic Numerals and Algebra | Zero to Infinity (Grades: 9-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eLearn where today’s widely used number system and basic math functions came from, and how the decimal system was developed. The set of ten numerals—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—that you have used all your life make up the Hindu-Arabic system, also known as the decimal system or base-ten system. It is a place value (or “positional”) system, meaning that the value of a numeral depends on its position. The values increase by powers of ten. For example, in the number 3,286, “6” is in the ones place while “3” is in the thousands place; the value of each numeral is its value multiplied by the value of the place—the “3” in the number represents 3,000.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-historyofzero/the-history-of-zero-zero-to-infinity/\"\u003e\u003cb\u003eThe History of Zero | Zero to Infinity (Grades: 6-8)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eAlthough it’s easy to take the concept of zero for granted, this digit representing “none” actually had to be invented. Learn about when and where the zero we use today originated.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-pizzacirclearea/calculating-the-area-of-a-circle-using-pizza-slices-zero-to-infinity/\"\u003e\u003cb\u003eCalculating the Area of a Circle Using Pizza Slices | Zero to Infinity (Grades: 6-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eFinding the area of a circle is easy with a simple formula involving pi. But how could people have done it before they knew about pi? Learn how the concept of infinity can help convert a circular pizza into a rectangle, making it much easier to measure. Use this resource to help students reason abstractly and construct an argument about the formula for the area of a circle.\u003c/p\u003e\n\u003ch3\u003e\u003ca href=\"https://ny.pbslearningmedia.org/resource/nvzti-sci-calculusparadoxeslimits/zenos-paradoxes-and-limits-in-calculus-zero-to-infinity/\"\u003e\u003cb\u003eZeno’s Paradoxes and Limits in Calculus | Zero to Infinity (Grades: 9-12)\u003c/b\u003e\u003c/a\u003e\u003c/h3\u003e\n\u003cp\u003eIn the fifth century BCE, the Greek philosopher Zeno of Elea thought deeply about time and motion. Zeno is most famous for describing several paradoxes where if one assumes space and time are infinitely divisible, then it follows that motion is an illusion. More than a thousand years after Zeno’s death, a new branch of mathematics called calculus helped make sense of his paradoxes. Use this resource to provide opportunities for students to calculate how fast an object is moving at a particular instant using limits in calculus.\u003c/p\u003e\n\u003cdiv class=\"newsletter\"\u003e\u003c/div\u003e","author":["kara-norton-"],"short_description":"\u003cp data-block-key=\"waalc\"\u003eFrom the ancient origins of zero to the paradox of motion, NOVA’s teaching resources immerse students in the wonder of math.\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"Teaching resources: How ancient cultures shaped mathematics","slug":"math-teaching-resources-zero-to-infinity","page_type":"article","canonical_image":{"mime_type":"image/jpeg","alt_text":"The hindu arabic numerals displayed on an ancient text","caption":{"html":"\u003cp\u003eThe numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH\u003c/p\u003e","plaintext":"The numeral system of 0 through 9 known as the Hindu–Arabic system, recognizes both the Hindu origin of the numerals and the role of Arab mathematicians in the Middle East who introduced it to Europe. Image Credit: NOVA/GBH"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.jpg","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/nvzti-vid-hinduarabicnumerals-poster_aXtJMOW.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1669930380000]},{"_index":"content","_type":"doc","_id":"article-6561","_score":null,"_source":{"slug":"math-thought-experiment-zero-infinity","title":"4 mind-bending math experiments that explain infinity","topic":"physics","brand":"next","content_type":"article","publish_date":"2022-11-29T16:55:12.595930+00:00","tags":["geometry","infinity","math","trigonometry","set theory","algebra","thought experiment","calculus"],"dci":["mathematical-sciences"],"external":false,"published":true,"hero_image":{"mime_type":"image/png","alt_text":"On a black background, a row of 6 red die lines up with a row of 6 red shoes, with white lines connecting them","caption":{"html":"\u003cp\u003eA set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA\u003c/p\u003e","plaintext":"A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/Set_theory_hero.png","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-300.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"content":"\u003cdiv class=\"related\"\u003e\u003c/div\u003e\n\u003cp\u003eIt can be easy to take math for granted. But the field has evolved over millennia, and concepts that seem obvious today had to be invented. Although zero is the beginning of counting, it arrived late to the math party. But not as late as its counterpart, infinity. Four thought experiments featured in NOVA’s “\u003ca href=\"https://www.pbs.org/wgbh/nova/video/zero-to-infinity/\"\u003eZero to Infinity\u003c/a\u003e” illustrate how people used the world around them to explore these revolutionary concepts.\u003c/p\u003e\n\u003ch3\u003e\u003cb\u003eHow infinity can help determine the area of a pizza (without pi) \u003c/b\u003e\u003c/h3\u003e\u003cp\u003ePizza is an interesting dish–a circle cut into triangles and served in a square box—an elusive mystery of early mathematics. Not the serving of the pizza, but the circle itself. See, squares and rectangles have straight lines, so it’s easy to determine their area. A circle, on the other hand, left ancient scholars scratching their heads. One solution: infinity.\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/cmd4wrtqDNaP6ev8jLbXJw==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eHilbert’s Hotel: Is there room for one more at a hotel with infinite rooms?\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eInfinity can be a tough concept to grasp. But mathematician David Hilbert came up with a more concrete way to think about it: A hotel with an infinite number of rooms–all occupied. What happens when one more guest shows up? What about an infinite number of guests, all evacuated from another nearby “Hilbert’s hotel” that caught on fire? Is there room for everyone?\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/kxjvkssttL0dWY49v-Ch6w==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cdiv class=\"ad\"\u003e\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eZeno’s Paradox: Infinity turns a speeding arrow into an illusion (25:44 - 30:24)\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eThe Greek philosopher Zeno of Elea came up with a paradox that questioned the very idea of motion. Suppose you shoot an arrow and try to calculate its speed. You need to divide the distance traveled by the amount of time elapsed. But supposing that instead of moving, the arrow is actually at rest for an infinity of instants, then you would be dividing by zero–which is against the rules of mathematics.\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/OP-VBloee-XyDYXck2GEMA==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003ch3\u003e\u003cb\u003eCantor’s Theorem: Some infinities are bigger than others (44:06 - 51:00)\u003c/b\u003e\u003c/h3\u003e\u003cp\u003eGerman mathematician Georg Cantor helped us think about how big infinity actually is. He created a concept called “set theory,” in which you have a defined collection, or \"set,\" of things, and if they match up one-to-one with another set of things, then both sets are the same size. But let’s say you take an infinite set of counting numbers (1,2,3…) and match it up to an infinite set of even numbers. Which one is bigger? It turns out they are exactly the same size. Here’s why:\u003c/p\u003e\n\u003cdiv class=\"cove-video\"\u003e\n\u003ciframe allow=\"encrypted-media\" allowfullscreen=\"\" class=\"inline-cove-player\" frameborder=\"0\" height=\"100%\" id=\"partnerPlayer\" marginheight=\"0\" marginwidth=\"0\" scrolling=\"no\" src=\"//player.pbs.org/partnerplayer/OP-VBloee-XyDYXck2GEMA==/?topbar=false\u0026amp;end=0\u0026amp;endscreen=true\u0026amp;start=0\u0026amp;autoplay=false\" width=\"100%\"\u003e\n\u003c/iframe\u003e\n\u003c/div\u003e\n\u003cdiv class=\"newsletter\"\u003e\u003c/div\u003e","author":["attabey-rodriguez-benitez"],"short_description":"\u003cp data-block-key=\"03b0f\"\u003eCan one infinity be bigger than another?\u003c/p\u003e","hits_weekly":0,"hits_daily":0,"card":{"title":"4 mind-bending math experiments that explain infinity","slug":"math-thought-experiment-zero-infinity","page_type":"article","canonical_image":{"mime_type":"image/png","alt_text":"On a black background, a row of 6 red die lines up with a row of 6 red shoes, with white lines connecting them","caption":{"html":"\u003cp\u003eA set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA\u003c/p\u003e","plaintext":"A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA"},"src":"https://www.pbs.org/wgbh/nova/media/original_images/Set_theory_hero.png","renditions":[{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-300.png","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-400.png","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-600.png","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-800.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-1500.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2000.png","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/Set_theory_hero.width-2500.png","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"contentType":"application/vnd.theseus+page"}},"sort":[1669740912595]}]},"current_filter":{"size":7,"from":0,"body":{"query":{"constant_score":{"filter":{"bool":{"must":[{"terms":{"topic":["physics"]}}],"should":[]}}}},"sort":{"publish_date":{"order":"desc"}}}},"query":{"page":"physics"},"featured_content":{"first":[{"content_type":"seriespage","topic":"physics","brand":"nova","title":"The Fabric of the Cosmos","slug":"the-fabric-of-the-cosmos","hero_image":{"mime_type":"image/jpeg","alt_text":"","caption":{"html":"\u003cp\u003e\u003c/p\u003e","plaintext":""},"credit":{"html":"\u003cp\u003e\u003c/p\u003e","plaintext":""},"src":"https://www.pbs.org/wgbh/nova/media/original_images/fabric-of-cosmos-merl2.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/fabric-of-cosmos-merl2.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"short_description":"\u003cp\u003eAcclaimed physicist Brian Greene reveals a mind-boggling reality beneath the surface of our everyday world.\u003c/p\u003e","long_description":"\u003cp\u003e\u003c/p\u003e\u003cp\u003e\"The Fabric of the Cosmos,\" a four-hour series based on the book by renowned physicist and author Brian Greene, takes us to the frontiers of physics to see how scientists are piecing together the most complete picture yet of space, time, and the universe. With each step, audiences will discover that just beneath the surface of our everyday experience lies a world we'd hardly recognize—a startling world far stranger and more wondrous than anyone expected.\u003c/p\u003e\u003cp\u003eBrian Greene is going to let you in on a secret: We've all been deceived. Our perceptions of time and space have led us astray. Much of what we thought we knew about our universe—that the past has already happened and the future is yet to be, that space is just an empty void, that our universe is the only universe that exists—just might be wrong.\u003c/p\u003e\u003cp\u003eInterweaving provocative theories, experiments, and stories with crystal-clear explanations and imaginative metaphors like those that defined the groundbreaking and highly acclaimed series \"The Elegant Universe,\" \"The Fabric of the Cosmos\" aims to be the most compelling, visual, and comprehensive picture of modern physics ever seen on television.\u003c/p\u003e","external":false}],"second":[{"content_type":"episodepage","topic":"space","brand":"nova","length":6765,"title":"Black Hole Apocalypse","slug":"black-hole-apocalypse","part_of_a_series":false,"hero_image":{"mime_type":"image/jpeg","alt_text":"","src":"https://www.pbs.org/wgbh/nova/media/original_images/black-hole-apocalypse-hero_I3y3xQu.jpg","renditions":[{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-2000.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1920,"height":1080,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-2500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":1500,"height":843,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-1500.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":800,"height":450,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-800.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":600,"height":337,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-600.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":400,"height":225,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-400.jpg","contentType":"application/vnd.theseus+scaled_image"},{"width":300,"height":168,"src":"https://www.pbs.org/wgbh/nova/media/images/black-hole-apocalypse-hero_I3y3xQu.width-300.jpg","contentType":"application/vnd.theseus+scaled_image"}],"contentType":"application/vnd.theseus+image"},"short_description":"\u003cp\u003eTake a mind-blowing voyage to the most powerful and mysterious objects in the universe.\u003c/p\u003e","long_description":"\u003cp\u003e\u003c/p\u003e\u003cp\u003eBlack holes are the most enigmatic and exotic objects in the universe. They’re also the most powerful, with gravity so strong it can trap light. And they’re destructive, swallowing entire planets, even giant stars. Anything that falls into them vanishes…gone forever. Now, astrophysicists are realizing that black holes may be essential to how our universe evolved—their influence possibly leading to life on Earth and, ultimately, us. In this two-hour special, astrophysicist and author Janna Levin takes viewers on a journey to the frontiers of black hole science. Along the way, we meet leading astronomers and physicists on the verge of finding new answers to provocative questions about these shadowy monsters: Where do they come from? What’s inside? What happens if you fall into one? And what can they tell us about the nature of space, time, and gravity? 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