This clip shows how each one of the five Platonic solids has the ability to contain the other four forms perfectly within it. Each form takes a turn as central, second out, third out, fourth out and all-encompassing fifth form out. This provides a beautiful example of the exquisite interconnectivity of all these forms. This is part of the 90 minutes Unity of Geometry video tutorial by Jonathan Quintin Five Platonic solid animation by Brett Orams The full video can be seen at vimeo.com The video can be purchased at www.sacredgeometry.com.au
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Texas School for the Blind and Visually Impaired Outreach Math Consultant Susan Osterhaus demonstrates techniques and introduces tools for working with math students who are blind, visually impaired, or deafblind.
PLATONIC SOLIDS AND MODELS OF CHEOPS PYRAMID IN BRASS ARTISTIC FEATURE. VIDEO TAKE IN THE ARTIST’S STUDIO: CESARE DEVITA IN LUGANO. ALSO SEE cesaredeitalugano08.blogspot.com
Believed to be sacred shapes irony is there all a division of Pi . π/3 = triangle π/4 = square π/5 = pentagon Euler’s Formula (yellow) tetrahedron F4 + V4 – E6 = 2 (orange) hexahedron / cube F6 + V8 – E12 = 2 (red, yellow) octahedron F8 + V6 – E12 = 2 (yellow ,green ,red) icosahedron F20 + V12 – E30 = 2 (blue) dodecahedron F12 + V20 – E30 = 2 centre shape (rhombicosidodecahedron) F62 + V60 – E120 = 2 All these shapes are included in anim8or primitives excluding rhombicosidodecahedron used in morph animation to generate them. www.anim8or.com
This continuous loop rotates around a nest of the five Platonic Solids: Cube (red), Tetrahedron (yellow), Octahedron (green), Icosahedron (blue) and Dodecahedron (purple), returning to a cube oriented along the same xyz axes one third the size in each dimension as the outer cube. The transparency of the inner cube changes from 100% opaque to 100% transparent as the animation proceeds, which allows playing as an infinte recursive loop. High-resolution versions and more info at www.geometrycode.com and www.brucerawles.com
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demonstrations.wolfram.com The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The 13 Archimedean solids are the only solids whose faces are composed of two or more distinct regular polygons placed in a symmetrical arrangement. Contributed by: Eric W. Weisstein
demonstrations.wolfram.com The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A maze on an Archimedean solid is given. The solid is projected on a sphere, which is projected into the plane using a map projection. Contributed by: Izidor Hafner
(This video is best viewed in HD. Music: Chopin’s Op. 28, Prelude 15, Sostenuto in D-flat major, or the “Raindrop Prelude”.) Software details and download page: www.numenta.com This is a network designed around the principle of Hierarchical Temporal Memory, a single algorithmic process inspired by the neocortex which uses a hierarchical structure to distribute memory of received inputs, essentially forming invariant representations of sufficiently stable stimuli or conditions. In other words, like the brain, it produces identifications of certain patterns with which it has been trained to recognize. Partly inspired by Jeff Hawkins’ description of Plato’s forms—that were assumed to be in some higher plane of existence—in his book “On Intelligence” and partly by curiosity, I gathered numerous images of the five Platonic Solids (or regular polyhedra) through polyhedra.org’s Canvas Element which are licensed under the GNU Free Documentation License. The regular polyhedra comprise the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, that is, five categories. After initial training and then optimization, this network was able to reach a 98.7% accuracy rating. In fact, optimization made no difference in this case. That said, this is markedly better than a mere guess! A guess would, statistically speaking, have only a 1 in 5 (or 20%) chance of being correct. As for Plato’s higher plane of existence, this surely turns it on its head. For more information visit …
Experiment # 1.62: Kinect, Processing, Simple OpenNI, 2 Icosahedrons. Code: www.openprocessing.org/visuals/?visualID=43513 Next step = setup Kinect above a client/subject on a massage table. Use video goggles so client can see the kinect’s perspective. Position platonic solids above various acupressure points. Conduct virtual acupressure session. Next Next step = add a hand tracking particle system. Intelligent Healing Spaces – Video Projection Therapy Development Blog: bit.ly/i1SJZ2 Special thanks to Ira Greenberg for the Icosahedron code, Max Rhenier for the SimpleNUI Processing wrapper, and to Shiffman for his new book, The Nature of Code.
We show how to define the Platonic Solids geometrically, observe their shapes and count their faces, edges, and vertices, and give a proof that these are the only five regular solids.
Video demonstrating how to make all the platonic solids using spherical magnets. Tetrahedron – 4 triangles. Cube – 6 x 6 x 6. Octahedron – 8 triangles. Dodecahedron – 12 pentagons. Icosahedron – 20 triangles.
In Part 8 The Intro of the 5 Platonic Solids. We discuss how the 5 Platonic Solids have a direct correlation to ourselves (the body), the planet, and the Universe. A quick glance at the Flower of Life and how it ties into the 5 Platonic Solids from which the Hexahedron, the Octahedron, Tetrahedron, Icosahedron, and the Dodecahedron come out of.
michael hansmeyer: subdivided cube 4 computational architecture: michael-hansmeyer.com original video: www.youtube.com audio: 1967 poem, booming back at you, junkie xl, 2008
How to make platonic solids with gum drops and tooth picks. Great project for kids!
MIT postdoctoral fellow Emily Peters discusses the Platonic solids, showing that there are only five of these special polyhedra. Emily points out that at 01:05, she tells a lie! How many triangular faces does the octahedron have? Conceived by Elisenda Grigsby, the Women In Mathematics (WIM) video series features women in math explaining some piece of math that interested them when they were in school. Often filmed on the spur of the moment, these videos showcase the diverse group of women working in mathematics today. For more WIM videos, please visit our website at www.girlsangle.org Presenting Emily Peters Filmed and Edited by Elisenda Grigsby Produced by Girls’ Angle. Corporate funding provided by Big George Ventures Philanthropy Fund. Copyright 2011 by Girls’ Angle.
www.bbc.co.uk In episode two of The Code Marcus du Sautoy takes a look at the Platonic Solids – five perfectly symmetrical solids, central to Greek geometry, that may look familiar to us today – the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron.
Out-of-print video on the Platonic Solids – prepared by the Visual Geometry Project.