Polyhedra and Euler's formula | Algebraic Topology | NJ Wildberger

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We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and flow down a sphere.
This is the eighth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.
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Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!
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Here are the Insights into Mathematics Playlists:
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Here are the Wild Egg Maths Playlists (some available only to Members!)
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Опубликовано:

1 авг 2024

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Комментарии : 13

@asimislam6194 Год назад

All of your lectures are outstanding! Super clear and very engaging and full of interest 👌

@KipIngram 10 месяцев назад

43:49 - That is a beautiful proof. Very "satisfying."

@allstargoldeneye 12 лет назад

what a teacher. Your filled with knowledge and wisdom.

@chiccocalleri 11 лет назад

Beautiful lesson indeed ! As i am a teacher in italian seccondary school I hope to bring something of this proof of Euler formula in my classes. Why not ?

@Reliquancy 11 лет назад

Wow that is a mind-blowing proof. I'd been asked whether I was related to William Thurston before but had never seen any of his ideas explained.

@njwildberger 11 лет назад

You obviously have some rare skill to make these lovely solids, thanks for letting us know.

@isabelweissman388 4 года назад

Super helpful!!

@njwildberger 11 лет назад

A billion dollars would be way to much, I wouldn't know what to do with it. Thanks for the support, and it is a nice idea!

@HerbBennett 2 года назад

Euler's FORMULA works for two face polygons and by cutting into the faces with two additional edges for a triangle we gat V-E+F =2 OR [3 -3 +2=2] bY CUTTING we add two edges for V-E+F =2 The cutting perpendicular from edge center to face center produces two new edges and one additional vertex following the flowing of charges. 4-5-+1=2. 1 represents the abstracted S2 plane as an imaginary singular dynamic.