Explore a fascinating 43-minute video that uncovers a stunning connection between Pythagorean triples and the Fibonacci sequence, discovered in 2007. Delve into topics such as the Pythagorean triple tree, Feuerbach's miracle, and the families of Plato, Fermat, and Pythagoras. Learn about Euclid's Elements and various proofs, while discovering why Fibonacci numbers are special. Engage with puzzles throughout the video, including a Fibonacci box challenge and a necklace puzzle. Gain insights into additional mathematical concepts like the relationship between Pythagorean triples and Pascal's triangle, and explore interesting properties of Fibonacci numbers. Benefit from supplementary resources, including research papers, Wikipedia articles, and interactive tools to further enhance your understanding of this captivating mathematical discovery.
Overview
Syllabus
Intro
Pythagorean triple tree
Pythagoras's other tree
Feuerbach miracle
Life lesson
The families of Plato, Fermat and Pythagoras
Euclid's Elements
Fibonacci numbers are special
Eugen Jost's spiral
Thank you!!!
Solution to my pearl necklace puzzle
- right circle doesn't touch line I mucked up :
Puzzle 1: a Fibonacci box of 153, 104, 185 b path from from 3, 4, 5, to this triple in the tree
Puzzle 2: Area of gen 5 Pythagorean tree
Puzzle 3: Necklace puzzle
theoriginalstoney and Michael Morad observed that at last section, extra special Fibonacci the difference between the two righthand numbers 4 and 5, 12 and 13, 30 and 34, 80 and 89 are also squares of the Fibonacci numbers: F_2n+3 - 2 F_n+1 F_n+2=F_n^2
Éric Bischoff comments that the trick to get a right angle at is popularized in French under the name "corde d'arpenteur". This term refers to a circular rope with 12 equally spaced nodes. If you pull 3, 4 and 5-node sides so the rope is tense, you get a right angle. See article "Corde à nœuds" on Wikipedia
Taught by
Mathologer
