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Proving Pick's Theorem | Infinite Series

2017-03-16

[public] 100.0K views, 3.40K likes, 58.0 dislikes audio only

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You could spend hours doing trigonometry to determine the area of a complex shape or you could simply plug in Pick’s Theorem.

Previous Episode - 5 Unusual Proofs

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Written and Hosted by Kelsey Houston-Edwards

Produced by Rusty Ward

Graphics by Ray Lux

Made by Kornhaber Brown (www.kornhaberbrown.com)

Sources and further references:

David Eppstein’s Math Fun

https://www.ics.uci.edu/~eppstein/recmath.html

Proofs from the Book by Martin Aigner and Günter M. Ziegler

https://www.amazon.com/Proofs-BOOK-Martin-Aigner/dp/3642008550

Comments answered by Kelsey:

J.H.

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M.K.D

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Computing the Euler characteristic of a planar graph
/youtube/video/bYW1zOMCQno?t=51
Euler characteristic defined to be
/youtube/video/bYW1zOMCQno?t=61
ALL Planar Graphs have Euler characteristic 2
/youtube/video/bYW1zOMCQno?t=220
the small triangles have area 1/2
/youtube/video/bYW1zOMCQno?t=345
STEP TWO
/youtube/video/bYW1zOMCQno?t=379
Find total number of small triangles
/youtube/video/bYW1zOMCQno?t=395
STEP THREE
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Euler's Formula
/youtube/video/bYW1zOMCQno?t=403