Pythagorean theorem: earrings

Pythagorean theorem has many famous proofs of the type “Look”. Some of them can be presented in a very unusual way.

One set must contain different earrings: together they present a proof of a Pythagor’s theorem. A girl with such earrings will surely attract atten­tion, and if she explains the theorem’s proof to a young man…

The same proof can be real­ized as a table model for a class.

Such a proof has been known since ancient times. Ancient Chinese “Trac­tate on a measuring pole” indi­cates, that Pythagorean theorem for a right triangle with sides $3$, $4$, $5$ was known by Shan Gao 1100 years BC, and in a common case — to Chan-Zi, who lived in VI century BC. In the comments to this book it is indi­cated that the proof of this theorem was based on a draft, illus­trated below (the left draft). And in an Indian book “A wreath of knowl­edge” (Bhaskara, XII century) the right draft is mentioned as a proof of a theorem, completed by a caption “Look”.

The mentioned images are only ideas for proofs. It is recom­mended to fully reestab­lish them in every case.

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