Polyhedra and Euler's formula | Algebraic Topology | NJ Wildberger
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- čas přidán 27. 07. 2024
- 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 all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: / playlist
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Year 9 Maths: • Year9Maths
Ancient Mathematics: • Ancient Mathematics
Wild West Banking: • Wild West Banking
Sociology and Pure Mathematics: • Sociology and Pure Mat...
Old Babylonian Mathematics (with Daniel Mansfield): / playlist
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Math History: • MathHistory: A course ...
Wild Trig: Intro to Rational Trigonometry: • WildTrig: Intro to Rat...
MathFoundations: • Math Foundations
Wild Linear Algebra: • Wild Linear Algebra
Famous Math Problems: • Famous Math Problems
Probability and Statistics: An Introduction: • Probability and Statis...
Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
Universal Hyperbolic Geometry: • Universal Hyperbolic G...
Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
Math Seminars: • MathSeminars
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And here are the Wild Egg Maths Playlists:
Triangle Centres: • ENCYCLOPEDIA OF TRIANG...
Six: An elementary course in pure mathematics: • Six: An elementary cou...
Algebraic Calculus One: • Algebraic Calculus One
Algebraic Calculus Two: • Algebraic Calculus Two
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All of your lectures are outstanding! Super clear and very engaging and full of interest 👌
43:49 - That is a beautiful proof. Very "satisfying."
what a teacher. Your filled with knowledge and wisdom.
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 ?
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.
You obviously have some rare skill to make these lovely solids, thanks for letting us know.
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!
Super helpful!!
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.
i didnt know about archemedean solids. i love them
very helpful thank you sir!
I don't really have a text that follows these lectures. Perhaps I should ask one of my former students who might have taken good notes..