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imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/2021.png" alt="Graph for 2021" title="Graph for 2021" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/farewell-2021-3n1">Farewell 2021 with 3n+1</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-2 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/robotic-arm"><a href="/content/robotic-arm" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/roboarm.png" alt="Robotic arm" title="Robotic arm" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/robotic-arm">Robotic arm</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-3 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/flying-boxes-0"><a href="/content/flying-boxes-0" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/flying_boxes.png" alt="flying boxes" title="flying boxes" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/flying-boxes-0">Flying boxes</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-4 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/newtons-cradle-twist"><a href="/content/newtons-cradle-twist" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/newton_cradle.png" alt="Newton's Cradle " title="Newton's Cradle" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/newtons-cradle-twist">Newton's cradle</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-5 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/pokestop"><a href="/content/pokestop" class="imagecache 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imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/involute-gear">involute gear</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">aplesch</span> </div> </li> <li class="jcarousel-item-7 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/bali-hut"><a href="/content/bali-hut" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/balihut.png" alt="Bali Hut" title="Bali Hut" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/bali-hut">Bali Hut</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-8 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/vrbox-world"><a href="/content/vrbox-world" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/vrbox_world.png" alt="VRBox world" title="VRBox world" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/vrbox-world">VRBox world</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-9 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/copper-lattice"><a href="/content/copper-lattice" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/copper_lattice.png" alt="Copper Lattice" title="Copper Lattice" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/copper-lattice">Copper Lattice</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-10 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/3d-involute-gears"><a href="/content/3d-involute-gears" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u342/image/involute_gear3.png" alt="3d gears" title="3d gears" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/3d-involute-gears">3d involute gears</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">aplesch</span> </div> </li> <li class="jcarousel-item-11 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/palm-tree"><a href="/content/palm-tree" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/palm.png" alt="Palm tree" title="Palm tree" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/palm-tree">Palm tree</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-12 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/spur-gears"><a href="/content/spur-gears" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/gear3d.png" alt="Spur gear set" title="Spur gear set" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/spur-gears">Spur gears</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-13 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/earth-cross-section"><a href="/content/earth-cross-section" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/earth_cross_section.png" alt="Earth Cross Section" title="Earth Cross Section" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/earth-cross-section">Earth Cross Section</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-14 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/waves-sea"><a href="/content/waves-sea" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/Sea_surface.png" alt="Sea surface" title="Sea surface" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/waves-sea">Waves at sea</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-15 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/analog-clock"><a href="/content/analog-clock" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/analog_clock.png" alt="Analog clock" title="Analog clock" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/analog-clock">Analog clock</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-16 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/hypercube-tesseract"><a href="/content/hypercube-tesseract" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/hypercube.png" alt="hypercube" title="hypercube" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/hypercube-tesseract">Hypercube - Tesseract</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-17 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/helium-atom"><a href="/content/helium-atom" class="imagecache 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imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/truncated-cube">Truncated cube</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">crystal h</span> </div> </li> <li class="jcarousel-item-19 odd"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/shield-or-spider-web"><a href="/content/shield-or-spider-web" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/rotating_cube_frames.png" alt="rotating cube frames" title="rotating cube frames" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/shield-or-spider-web">A shield or spider web?</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">Andy</span> </div> </li> <li class="jcarousel-item-20 even"> <div class="views-field-field-image-fid"> <span class="field-content"><a href="/content/truncated-icosidodecahedron"><a href="/content/truncated-icosidodecahedron" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u177/image/Capture.PNG" alt="Image ALT text" title="Image Title Text" width="146" height="110" class="imagecache imagecache-146x110"/></a></a></span> </div> <div class="views-field-title"> <span class="field-content"><a href="/content/truncated-icosidodecahedron">Truncated</a></span> </div> <div class="views-field-name"> <label class="views-label-name"> Created by: </label> <span class="field-content">advercis</span> </div> </li> </ul> </div> </div> </div> </div> </div> </div> </div> <div id="navigation"> 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row nested"> <div id="main-content-inner" class="main-content-inner inner">  <div id="content-group" class="content-group row nested grid16-16"> <div id="content-group-inner" class="content-group-inner inner"> <div id="content-region" class="content-region row nested "> <div id="content-region-inner" class="content-region-inner inner"> <a name="main-content-area" id="main-content-area"></a> <div id="content-inner" class="content-inner block"> <div id="content-inner-inner" class="content-inner-inner inner"> <h1 class="title">Blogs</h1> <div id="content-content" class="content-content"> <div class="item-list"></div> <div id="node-572" class="node odd teaser node-type-blog"> <div class="inner"> <div class="picture"> <img src="https://vrmath2.net/sites/default/files/imagecache/50x50/pictures/picture-708.jpg" alt="dpietrobon's picture" title="dpietrobon's picture" width="50" height="50" class="imagecache imagecache-50x50"/></div> <h2 class="title"><a href="/content/prisms-and-antiprisms" title="Prisms and Antiprisms">Prisms and Antiprisms</a></h2> <div class="meta"> <span class="submitted">Submitted by dpietrobon on Sat, 01/03/2025 - 15:36</span> <div class="terms"><ul class="links inline"><li class="taxonomy_term_578 first"><a href="/tags/antiprisms" rel="tag" title=""><span>antiprisms</span></a></li> <li class="taxonomy_term_180"><a href="/tags/logo" rel="tag" title=""><span>Logo</span></a></li> <li class="taxonomy_term_577"><a href="/tags/prisms" rel="tag" title=""><span>prisms</span></a></li> <li class="taxonomy_term_121"><a href="/categories/mathematics/geometry" rel="tag" title=""><span>Geometry</span></a></li> <li class="taxonomy_term_116 last"><a href="/categories/mathematics" rel="tag" title=""><span>Mathematics</span></a></li> </ul></div> </div> <div class="content clearfix"> <div class="field field-type-filefield field-field-image"> <div class="field-items"> <div class="field-item odd"> <a href="/content/prisms-and-antiprisms" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u708/image/turtle05.png" alt="" title="" width="146" height="110" class="imagecache imagecache-146x110"/></a> </div> </div> </div> <p dir="ltr" style="line-height:1.656;margin-top:9pt;margin-bottom:9pt;"><span id="docs-internal-guid-e8c643b5-7fff-fe54-87b4-cee6fbeff9f7"><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);">A </span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-weight: 700; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);">prism</span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);"> is a 3D shape with two matching polygonal faces connected by straight edges.</span></span></p> <p dir="ltr" style="line-height:1.656;margin-top:9pt;margin-bottom:9pt;"><x3d src="/sites/default/files/user/u708/x3d/prisms03.x3d" type="model/x3d+xml"><scene><inline namespacename="CIHH" url="/sites/default/files/user/u708/x3d/prisms03.x3d"></inline></scene></x3d></p> <p dir="ltr" style="line-height:1.656;margin-top:9pt;margin-bottom:9pt;"> </div> <div class="node-links clearfix"> <ul class="links inline"><li class="blog_usernames_blog first"><a href="/blogs/dpietrobon" title="Read dpietrobon's latest blog entries."><span>dpietrobon's blog</span></a></li> <li class="comment_forbidden"><span><a href="/user/login?destination=comment%2Freply%2F572%23comment-form"><span>Login</span></a> <span class="regulat-text">or</span> <a href="/user/register?destination=comment%2Freply%2F572%23comment-form"><span>register</span></a> <span class="regulat-text">to post comments</span></span></li> <li class="node_read_more"><a href="/content/prisms-and-antiprisms" title="Read the rest of Prisms and Antiprisms."><span>Read more</span></a></li> <li class="statistics_counter last"><span>256 reads</span></li> </ul> </div> </div> </div> <div id="node-571" class="node even teaser node-type-blog"> <div class="inner"> <div class="picture"> <img src="https://vrmath2.net/sites/default/files/imagecache/50x50/pictures/picture-708.jpg" alt="dpietrobon's picture" title="dpietrobon's picture" width="50" height="50" class="imagecache imagecache-50x50"/></div> <h2 class="title"><a href="/content/regular-polygons" title="Regular Polygons">Regular Polygons</a></h2> <div class="meta"> <span class="submitted">Submitted by dpietrobon on Sat, 22/02/2025 - 14:06</span> <div class="terms"><ul class="links inline"><li class="taxonomy_term_421 first"><a href="/tags/geometry" rel="tag" title=""><span>Geometry</span></a></li> <li class="taxonomy_term_180"><a href="/tags/logo" rel="tag" title=""><span>Logo</span></a></li> <li class="taxonomy_term_582"><a href="/tags/logo-programming" rel="tag" title=""><span>logo programming</span></a></li> <li class="taxonomy_term_579"><a href="/tags/polygon" rel="tag" title=""><span>polygon</span></a></li> <li class="taxonomy_term_576"><a href="/tags/polygons" rel="tag" title=""><span>polygons</span></a></li> <li class="taxonomy_term_424"><a href="/tags/programming" rel="tag" title=""><span>Programming</span></a></li> <li class="taxonomy_term_580"><a href="/tags/regular-polygons" rel="tag" title=""><span>regular polygons</span></a></li> <li class="taxonomy_term_430"><a href="/tags/science" rel="tag" title=""><span>science</span></a></li> <li class="taxonomy_term_111"><a href="/categories/science" rel="tag" title=""><span>Science</span></a></li> <li class="taxonomy_term_221"><a href="/tags/shapes" rel="tag" title=""><span>shapes</span></a></li> <li class="taxonomy_term_505"><a href="/tags/visualisation" rel="tag" title=""><span>Visualisation</span></a></li> <li class="taxonomy_term_581"><a href="/tags/vrmath-0" rel="tag" title=""><span>vrmath</span></a></li> <li class="taxonomy_term_121"><a href="/categories/mathematics/geometry" rel="tag" title=""><span>Geometry</span></a></li> <li class="taxonomy_term_128"><a href="/categories/engineering/programming" rel="tag" title=""><span>Programming</span></a></li> <li class="taxonomy_term_120"><a href="/categories/engineering/visualisation" rel="tag" title=""><span>Visualisation</span></a></li> <li class="taxonomy_term_116 last"><a href="/categories/mathematics" rel="tag" title=""><span>Mathematics</span></a></li> </ul></div> </div> <div class="content clearfix"> <div class="field field-type-filefield field-field-image"> <div class="field-items"> <div class="field-item odd"> <a href="/content/regular-polygons" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u708/image/Screenshot%202025-02-22%20140328_0.png" alt="Image ALT text" title="Image Title Text" width="146" height="110" class="imagecache imagecache-146x110"/></a> </div> </div> </div> <p dir="ltr" style="line-height:1.656;margin-top:9pt;margin-bottom:9pt;"><span id="docs-internal-guid-43a5b067-7fff-abcd-a711-c83ece9a6298"><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);">A </span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-weight: 700; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);">polygon</span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);"> is a closed shape formed by straight lines. A </span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-weight: 700; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);">regular</span><span data-darkreader-inline-color="" style="font-size: 9pt; font-family: Arial, sans-serif; color: rgb(0, 0, 0); font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-variant-position: normal; font-variant-emoji: normal; vertical-align: baseline; white-space-collapse: preserve; --darkreader-inline-color: var(--darkreader-text-000000, #e8e6e3);"> polygon has sides of equal length and angles of equal size. Convex regular polygons are the common shapes we associate with 3, 4, 5, or more sides, such as the equilateral triangle, square, pentagon, hexagon, and so on.</span></span></p> <p dir="ltr" style="line-height: 1.656; margin-top: 9pt; margin-bottom: 9pt; text-align: center;"><x3d height="300px" src="/sites/default/files/user/u708/x3d/polygons03.x3d" type="model/x3d+xml" width="400px"><scene><inline namespacename="06j8" url="/sites/default/files/user/u708/x3d/polygons03.x3d"></inline></scene></x3d></p> <p dir="ltr" style="line-height: 1.656; margin-top: 9pt; margin-bottom: 9pt; text-align: center;"> </p> <p> </div> <div class="node-links clearfix"> <ul class="links inline"><li class="blog_usernames_blog first"><a href="/blogs/dpietrobon" title="Read dpietrobon's latest blog entries."><span>dpietrobon's blog</span></a></li> <li class="comment_comments"><a href="/content/regular-polygons#comments" title="Jump to the first comment of this posting."><span>2 comments</span></a></li> <li class="node_read_more"><a href="/content/regular-polygons" title="Read the rest of Regular Polygons."><span>Read more</span></a></li> <li class="statistics_counter last"><span>397 reads</span></li> </ul> </div> </div> </div> <div id="node-" class="node odd node-unpublished teaser node-type-"> <div class="inner"> <h2 class="title"><a href="/content/test-02" title=""></a></h2> <div class="content clearfix"> n/a </div> </div> </div> <div id="node-565" class="node even teaser node-type-blog"> <div class="inner"> <div class="picture"> <img src="https://vrmath2.net/sites/default/files/imagecache/50x50/pictures/picture-3.png" alt="Andy's picture" title="Andy's picture" width="50" height="50" class="imagecache imagecache-50x50"/></div> <h2 class="title"><a href="/content/3d-snowflake" title="3D Snowflake">3D Snowflake</a></h2> <div class="meta"> <span class="submitted">Submitted by Andy on Fri, 29/12/2023 - 22:44</span> <div class="terms"><ul class="links inline"><li class="taxonomy_term_87 first"><a href="/taxonomy/term/87" rel="tag" title=""><span>Fractal 3D</span></a></li> <li class="taxonomy_term_572"><a href="/tags/snowflake" rel="tag" title=""><span>Snowflake</span></a></li> <li class="taxonomy_term_121"><a href="/categories/mathematics/geometry" rel="tag" title=""><span>Geometry</span></a></li> <li class="taxonomy_term_116 last"><a href="/categories/mathematics" rel="tag" title=""><span>Mathematics</span></a></li> </ul></div> </div> <div class="content clearfix"> <div class="field field-type-filefield field-field-image"> <div class="field-items"> <div class="field-item odd"> <a href="/content/3d-snowflake" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u1/image/snowflake_extrusion.png" alt="Koch's snowflake extruded" title="Koch's snowflake extrusion" width="146" height="110" class="imagecache imagecache-146x110"/></a> </div> </div> </div> <p><span style="font-size:24px;">I</span>t is Christmas season, and it is deadly hot in Brisbane today (29 December 2023) at 39 degrees celsius in the southern hemisphere. I miss and wonder a snowy Christmas in norther hemisphere could be like. Perhaps making a snowflake could cool down my mind. It is also after about 2 years that I have not blogged in this VRMath2 website.</p><p> </div> <div class="node-links clearfix"> <ul class="links inline"><li class="blog_usernames_blog first"><a href="/blogs/andy" title="Read Andy's latest blog entries."><span>Andy's blog</span></a></li> <li class="comment_forbidden"><span><a href="/user/login?destination=comment%2Freply%2F565%23comment-form"><span>Login</span></a> <span class="regulat-text">or</span> <a href="/user/register?destination=comment%2Freply%2F565%23comment-form"><span>register</span></a> <span class="regulat-text">to post comments</span></span></li> <li class="node_read_more"><a href="/content/3d-snowflake" title="Read the rest of 3D Snowflake."><span>Read more</span></a></li> <li class="statistics_counter last"><span>2247 reads</span></li> </ul> </div> </div> </div> <div id="node-563" class="node odd teaser node-type-blog"> <div class="inner"> <div class="picture"> <img src="https://vrmath2.net/sites/default/files/imagecache/50x50/pictures/picture-3.png" alt="Andy's picture" title="Andy's picture" width="50" height="50" class="imagecache imagecache-50x50"/></div> <h2 class="title"><a href="/content/farewell-2021-3n1" title="Farewell 2021 with 3n+1">Farewell 2021 with 3n+1</a></h2> <div class="meta"> <span class="submitted">Submitted by Andy on Fri, 31/12/2021 - 13:28</span> <div class="terms"><ul class="links inline"><li class="taxonomy_term_571 first"><a href="/tags/3n-1-conjecture" rel="tag" title=""><span>3n + 1 conjecture</span></a></li> <li class="taxonomy_term_570"><a href="/tags/3n-1-problem" rel="tag" title=""><span>3n + 1 problem</span></a></li> <li class="taxonomy_term_123"><a href="/categories/mathematics/algebra" rel="tag" title=""><span>Algebra</span></a></li> <li class="taxonomy_term_568"><a href="/tags/collatz-conjecture" rel="tag" title=""><span>Collatz conjecture</span></a></li> <li class="taxonomy_term_569"><a href="/tags/sequences-integers" rel="tag" title=""><span>sequences of integers</span></a></li> <li class="taxonomy_term_121"><a href="/categories/mathematics/geometry" rel="tag" title=""><span>Geometry</span></a></li> <li class="taxonomy_term_125"><a href="/categories/mathematics/number" rel="tag" title=""><span>Number</span></a></li> <li class="taxonomy_term_116 last"><a href="/categories/mathematics" rel="tag" title=""><span>Mathematics</span></a></li> </ul></div> </div> <div class="content clearfix"> <div class="field field-type-filefield field-field-image"> <div class="field-items"> <div class="field-item odd"> <a href="/content/farewell-2021-3n1" class="imagecache imagecache-146x110 imagecache-linked imagecache-146x110_linked"><img src="https://vrmath2.net/sites/default/files/imagecache/146x110/user/u3/image/2021.png" alt="Graph for 2021" title="Graph for 2021" width="146" height="110" class="imagecache imagecache-146x110"/></a> </div> </div> </div> <p><span style="font-size:24px;">T</span>he Youtube algorithm one day pushed a video "<a href="https://www.youtube.com/watch?v=094y1Z2wpJg" target="_blank">The Simplest Math Problem No One Can Solve - Collatz Conjecture</a>" to me. After viewing the video, I thought that my VRMath2 could easily visualise the 3n+1 graph with its LOGO programing. I am happy that my VRMath2 application is still working after almost three years in low maintenance mode. With some simple coding. I have written a LOGO program that can take a number (natural number) and the turtle will draw its 3n+1 graph. The 3n+1 problem is simple. It starts with a natural number; if the number is odd, multiply it by 3 then add one; if the number is even, the number is divided by 2. These rules apply until the resulting number is one. It is interesting that it seems any given natural number will end with 1 after applying the 3n+1 rules, but how?</p> <p> </div> <div class="node-links clearfix"> <ul class="links inline"><li class="blog_usernames_blog first"><a href="/blogs/andy" title="Read Andy's latest blog entries."><span>Andy's blog</span></a></li> <li class="comment_forbidden"><span><a href="/user/login?destination=comment%2Freply%2F563%23comment-form"><span>Login</span></a> <span class="regulat-text">or</span> <a href="/user/register?destination=comment%2Freply%2F563%23comment-form"><span>register</span></a> <span class="regulat-text">to post comments</span></span></li> <li class="node_read_more"><a href="/content/farewell-2021-3n1" title="Read the rest of Farewell 2021 with 3n+1."><span>Read more</span></a></li> <li class="statistics_counter last"><span>4732 reads</span></li> </ul> </div> </div> </div> <div class="item-list"><ul class="pager"><li class="pager-current first">1</li> <li class="pager-item"><a 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