What is...Polya’s theorem?
Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...Polya’s theorem? Or: Birds get lost.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
Random walk.
https://www.ime.unicamp.br/~popov/2sr...
https://en.wikipedia.org/wiki/Random_...
Expected value and distance.
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
Polya’s constant.
https://mathworld.wolfram.com/PolyasR...
1d random walk a.k.a. coin flipping.
https://en.wikipedia.org/wiki/Coin_fl...
https://people.duke.edu/~rnau/411rand...
https://mathworld.wolfram.com/RandomW...
/ random-walk-a-comprehensive-illustration
https://blogs.sas.com/content/iml/201...
https://mathstrek.blog/2012/10/12/ran...
/ the-drunkards-walk-explained
2d random walk.
https://mathworld.wolfram.com/RandomW...
https://www.bragitoff.com/2021/05/ran...
https://math.stackexchange.com/questi...
3d random walk.
https://mathoverflow.net/questions/45...
• Visualizing Random Walks in Three Dimensions
Paris (size).
https://en.wikipedia.org/wiki/Paris_m...
Mathematica.
https://demonstrations.wolfram.com/Si...
https://demonstrations.wolfram.com/La...
https://demonstrations.wolfram.com/Ra...
https://demonstrations.wolfram.com/Se...
https://demonstrations.wolfram.com/Co...
Pictures used.
https://en.wikipedia.org/wiki/Coin_fl...
https://people.duke.edu/~rnau/411rand...
https://mathworld.wolfram.com/images/...
https://mathworld.wolfram.com/images/...
https://www.mapdevelopers.com/draw-ci...
Random walks are very popular.
• What is a Random Walk? | Infinite Series
• Why Do Random Walks Get Lost in 3D?
• The diffusion equation | Week 12 | MIT 18....