Why are Fibonacci numbers in this Random Walk?
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Link to the video that inspired this problem from the "Compass Mathematics" channel: https://youtu.be/AU8NZykX5rk . (And extra thanks Compass Mathematics for the nice back in forth in the comments of the original video before the re-upload!)
Why are the Fibonacci numbers hidden in this random walk on a pentagon? We'll find out by using a common trick when counting paths for random walks.
Chapters
0:00 Fibonacci fractions
0:40 Spider random walk on a pentagon
3:48 Unfold the pentagon to a line
7:05 Counting paths using sums
11:09 Proof by induction
Видео Why are Fibonacci numbers in this Random Walk? канала Dr Mihai Nica
Link to the video that inspired this problem from the "Compass Mathematics" channel: https://youtu.be/AU8NZykX5rk . (And extra thanks Compass Mathematics for the nice back in forth in the comments of the original video before the re-upload!)
Why are the Fibonacci numbers hidden in this random walk on a pentagon? We'll find out by using a common trick when counting paths for random walks.
Chapters
0:00 Fibonacci fractions
0:40 Spider random walk on a pentagon
3:48 Unfold the pentagon to a line
7:05 Counting paths using sums
11:09 Proof by induction
Видео Why are Fibonacci numbers in this Random Walk? канала Dr Mihai Nica
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30 апреля 2025 г. 15:12:29
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