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class="hid"> <h2 class="yt-card-title"> Transcript </h2> <div id="caption-line-template" class="hid">  </div> <div id="watch-transcript-container" class="yt-scrollbar"> <div id="watch-transcript-not-found" class="hid"> The interactive transcript could not be loaded. </div> </div> </div> </div> <div id="action-panel-report" class="action-panel-content hid" data-auth-required="true"> <div class="action-panel-loading"> <p class="yt-spinner "> <span class="yt-spinner-img yt-sprite" title="Loading icon"></span> <span class="yt-spinner-message"> Loading... </span> </p> </div> </div> <div id="action-panel-rental-required" class="action-panel-content hid"> <div id="watch-actions-rental-required"> <strong>Rating is available when the video has been rented.</strong> </div> </div> <div id="action-panel-error" class="action-panel-content hid"> <div class="action-panel-error"> This feature is not available right now. Please try again later. </div> </div> <button class="yt-uix-button yt-uix-button-size-default yt-uix-button-default yt-uix-button-empty yt-uix-button-has-icon no-icon-markup yt-uix-button-opacity yt-uix-close" type="button" onclick=";return false;" id="action-panel-dismiss" aria-label="Close" data-close-parent-id="watch8-action-panels"></button> </div> <div id="promotion-shelf" class="promotion-shelf-slot yt-card yt-card-has-padding hid"></div> <div id="action-panel-details" class="action-panel-content yt-uix-expander yt-card yt-card-has-padding yt-uix-expander-collapsed"><div id="watch-description" class="yt-uix-button-panel"><div id="watch-description-content"><div id="watch-description-clip"><div id="watch-uploader-info"><strong class="watch-time-text">Published on Dec 2, 2018</strong></div><div id="watch-description-text" class=""><p id="eow-description" class="">The formula is no mere coincidence.<br/>Store: <a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fstore&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fstore&event=video_description" target="_blank" rel="nofollow noopener">http://3b1b.co/store</a><br/>Home page: <a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fwww.3blue1brown.com&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fwww.3blue1brown.com&event=video_description" target="_blank" rel="nofollow noopener">https://www.3blue1brown.com</a><br/>Special thanks: <a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fsphere-thanks&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fsphere-thanks&event=video_description" target="_blank" rel="nofollow noopener">http://3b1b.co/sphere-thanks</a><br/><br/>Discussion on Reddit: <a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fwww.reddit.com%2Fr%2F3Blue1Brown%2Fcomments%2Fa2gqo0%2Fbut_why_is_a_spheres_surface_area_four_times_its%2F&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fwww.reddit.com%2Fr%2F3Blue1Brown%2Fcomments%2Fa2gqo0%2Fbut_why_is_a_spheres_surface_area_four_times_its%2F&event=video_description" target="_blank" rel="nofollow noopener">https://www.reddit.com/r/3Blue1Brown/...</a><br/><br/>The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:<br/><a href="/web/20200309152538/https://www.youtube.com/watch?v=KZJw0AYn6_k" class="yt-uix-sessionlink spf-link " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuQ">https://youtu.be/KZJw0AYn6_k</a><br/><br/>Calculus series:<br/><a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fcalculus&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=http%3A%2F%2F3b1b.co%2Fcalculus&event=video_description" target="_blank" rel="nofollow noopener">http://3b1b.co/calculus</a><br/><br/>Thanks to these folks for letting me use their images at the end:<br/><a href="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/vlogbrothers" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-url="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/vlogbrothers">https://www.youtube.com/user/vlogbrot...</a><br/><a href="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/physicswoman" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-url="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/physicswoman">https://www.youtube.com/user/physicsw...</a><br/><a href="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/Vsauce" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-url="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/Vsauce">https://www.youtube.com/user/Vsauce</a><br/><a href="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/onemeeeliondollars" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-url="https://web.archive.org/web/20200309152538/https://www.youtube.com/user/onemeeeliondollars">https://www.youtube.com/user/onemeeel...</a><br/><br/>------------------<br/><br/>These animations are largely made using manim, a scrappy open source python library: <a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fgithub.com%2F3b1b%2Fmanim&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fgithub.com%2F3b1b%2Fmanim&event=video_description" target="_blank" rel="nofollow noopener">https://github.com/3b1b/manim</a><br/><br/>If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.<br/><br/>Music by Vincent Rubinetti.<br/>Download the music on Bandcamp:<br/><a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fvincerubinetti.bandcamp.com%2Falbum%2Fthe-music-of-3blue1brown&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fvincerubinetti.bandcamp.com%2Falbum%2Fthe-music-of-3blue1brown&event=video_description" target="_blank" rel="nofollow noopener">https://vincerubinetti.bandcamp.com/a...</a><br/><br/>Stream the music on Spotify:<br/><a href="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fopen.spotify.com%2Falbum%2F1dVyjwS8FBqXhRunaG5W5u&event=video_description" class="yt-uix-sessionlink " data-sessionlink="itct=CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg" data-target-new-window="True" data-url="/web/20200309152538/https://www.youtube.com/redirect?v=GNcFjFmqEc8&redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4&q=https%3A%2F%2Fopen.spotify.com%2Falbum%2F1dVyjwS8FBqXhRunaG5W5u&event=video_description" target="_blank" rel="nofollow noopener">https://open.spotify.com/album/1dVyjw...</a><br/><br/>If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.<br/><br/>------------------<br/><br/>3blue1brown is a channel about animating math, in all senses of the word animate. 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yt-uix-sessionlink spf-link " data-sessionlink="itct=CBwQpDAYCSITCI_-nezZjegCFcbCxAodSEsEuTIHcmVsYXRlZEjPo6jNxbHB6xg" tabindex="-1" rel=" spf-prefetch nofollow" data-visibility-tracking="CBwQpDAYCSITCI_-nezZjegCFcbCxAodSEsEuUDhsdf77Jn_lHw=" aria-hidden="true"><span class="yt-uix-simple-thumb-wrap yt-uix-simple-thumb-related" data-vid="fCn8zs912OE"><img aria-hidden="true" data-thumb="https://web.archive.org/web/20200309152538/https://i.ytimg.com/vi/fCn8zs912OE/hqdefault.jpg?sqp=-oaymwEiCKgBEF5IWvKriqkDFQgBFQAAAAAYASUAAMhCPQCAokN4AQ==&rs=AOn4CLAem-hd9mbh2iTfU2fMjawfU8kLJQ" height="94" width="168" src="/web/20200309152538im_/https://www.youtube.com/yts/img/pixel-vfl3z5WfW.gif" style="top: 0px" alt=""><span class="video-time">21:05</span></span></a> </div> </li><li class="video-list-item related-list-item show-video-time related-list-item-compact-video"> <div class="content-wrapper"> <a href="/web/20200309152538/https://www.youtube.com/watch?v=IJhgZBn-LHg" class=" content-link spf-link 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\"},{\"text\":\"http:\/\/3b1b.co\/sphere-thanks\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fsphere-thanks\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nDiscussion on Reddit: \"},{\"text\":\"https:\/\/www.reddit.com\/r\/3Blue1Brown\/...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fwww.reddit.com%2Fr%2F3Blue1Brown%2Fcomments%2Fa2gqo0%2Fbut_why_is_a_spheres_surface_area_four_times_its%2F\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nThe first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2\/3 the volume of a cylinder encompassing it, and 2\/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:\\n\"},{\"text\":\"https:\/\/youtu.be\/KZJw0AYn6_k\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuQ==\",\"watchEndpoint\":{\"videoId\":\"KZJw0AYn6_k\"}}},{\"text\":\"\\n\\nCalculus series:\\n\"},{\"text\":\"http:\/\/3b1b.co\/calculus\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fcalculus\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nThanks to these folks for letting me use their images at the end:\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/vlogbrot...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/vlogbrothers\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/physicsw...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/physicswoman\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/Vsauce\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/Vsauce\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/onemeeel...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/onemeeeliondollars\"}}},{\"text\":\"\\n\\n------------------\\n\\nThese animations are largely made using manim, a scrappy open source python library: \"},{\"text\":\"https:\/\/github.com\/3b1b\/manim\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fgithub.com%2F3b1b%2Fmanim\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nIf you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.\\n\\nMusic by Vincent Rubinetti.\\nDownload the music on Bandcamp:\\n\"},{\"text\":\"https:\/\/vincerubinetti.bandcamp.com\/a...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fvincerubinetti.bandcamp.com%2Falbum%2Fthe-music-of-3blue1brown\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nStream the music on Spotify:\\n\"},{\"text\":\"https:\/\/open.spotify.com\/album\/1dVyjw...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fopen.spotify.com%2Falbum%2F1dVyjwS8FBqXhRunaG5W5u\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nIf you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles\/cc, then \\\"add subtitles\/cc\\\". I really appreciate those who do this, as it helps make the lessons accessible to more people.\\n\\n------------------\\n\\n3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: \"},{\"text\":\"http:\/\/3b1b.co\/subscribe\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fsubscribe\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nVarious social media stuffs:\\nWebsite: \"},{\"text\":\"https:\/\/www.3blue1brown.com\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CC4Q6TgYACITCI_-nezZjegCFcbCxAodSEsEuUjPo6jNxbHB6xg=\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fwww.3blue1brown.com\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\nTwitter: 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\"},{\"text\":\"http:\/\/3b1b.co\/sphere-thanks\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fsphere-thanks\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nDiscussion on Reddit: \"},{\"text\":\"https:\/\/www.reddit.com\/r\/3Blue1Brown\/...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fwww.reddit.com%2Fr%2F3Blue1Brown%2Fcomments%2Fa2gqo0%2Fbut_why_is_a_spheres_surface_area_four_times_its%2F\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nThe first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2\/3 the volume of a cylinder encompassing it, and 2\/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof:\\n\"},{\"text\":\"https:\/\/youtu.be\/KZJw0AYn6_k\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLk=\",\"watchEndpoint\":{\"videoId\":\"KZJw0AYn6_k\"}}},{\"text\":\"\\n\\nCalculus series:\\n\"},{\"text\":\"http:\/\/3b1b.co\/calculus\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fcalculus\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nThanks to these folks for letting me use their images at the end:\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/vlogbrot...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/vlogbrothers\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/physicsw...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/physicswoman\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/Vsauce\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/Vsauce\"}}},{\"text\":\"\\n\"},{\"text\":\"https:\/\/www.youtube.com\/user\/onemeeel...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"https:\/\/www.youtube.com\/user\/onemeeeliondollars\"}}},{\"text\":\"\\n\\n------------------\\n\\nThese animations are largely made using manim, a scrappy open source python library: \"},{\"text\":\"https:\/\/github.com\/3b1b\/manim\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fgithub.com%2F3b1b%2Fmanim\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nIf you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.\\n\\nMusic by Vincent Rubinetti.\\nDownload the music on Bandcamp:\\n\"},{\"text\":\"https:\/\/vincerubinetti.bandcamp.com\/a...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fvincerubinetti.bandcamp.com%2Falbum%2Fthe-music-of-3blue1brown\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nStream the music on Spotify:\\n\"},{\"text\":\"https:\/\/open.spotify.com\/album\/1dVyjw...\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fopen.spotify.com%2Falbum%2F1dVyjwS8FBqXhRunaG5W5u\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nIf you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles\/cc, then \\\"add subtitles\/cc\\\". I really appreciate those who do this, as it helps make the lessons accessible to more people.\\n\\n------------------\\n\\n3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: \"},{\"text\":\"http:\/\/3b1b.co\/subscribe\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=http%3A%2F%2F3b1b.co%2Fsubscribe\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\n\\nVarious social media stuffs:\\nWebsite: \"},{\"text\":\"https:\/\/www.3blue1brown.com\",\"navigationEndpoint\":{\"clickTrackingParams\":\"CCsQ4IgCGAAiEwiP_p3s2Y3oAhXGwsQKHUhLBLlIz6OozcWxwesY\",\"urlEndpoint\":{\"url\":\"\/redirect?v=GNcFjFmqEc8\\u0026redir_token=9Mz4lQ-xQwcSTgGdl849nE6tiRZ8MTU4Mzg1MzkzOEAxNTgzNzY3NTM4\\u0026q=https%3A%2F%2Fwww.3blue1brown.com\\u0026event=video_description\",\"target\":\"TARGET_NEW_WINDOW\"}}},{\"text\":\"\\nTwitter: 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