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Pythagoras Twisted Squares - Why Did They Not Teach You Any of This in School?

Mathologer via YouTube

Overview

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Explore the hidden depths of the iconic twisted squares diagram in this 39-minute video by Mathologer. Delve into advanced mathematical concepts like Fermat's four squares theorem, Pythagoras for 60- and 120-degree triangles, and the four bugs problem using twisted squares. Discover beautiful and important aspects of mathematics often overlooked in traditional education. Follow along as the video breaks down complex topics into digestible segments, including trithagoras, hexagoras, twisted square dissection proofs, and unusual applications of twisted squares. Engage with the final puzzle and witness an animation of the Cauchy-Schwarz proof. Gain access to additional resources and references for further exploration of the topics covered.

Syllabus

Intro.
3 Squares: Fermat's four square theorem.
Trithagoras.
Hexagoras.
Chop it up: More twisted square dissection proofs.
Aha! Remarkable properties of right triangles with a twist.
Mutants: Unusual applications of twisted squares.
Op art: The four bugs problem.
Final puzzle.
Animation of Cauchy-Schwarz proof.
Thanks!!.

Taught by

Mathologer

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