Math

Pythagoras by area

Three ways to compare areas: wooden pieces, flexible sheets, and an exact top view.

Actual application image

What happens

First assemble Perigal yourself. Watch one transfer, then retry without outlines. Change a/b: can you make a² exactly 25% of c²? Each transfer pauses before lifting; the shared Pause button freezes it. Number and colour identify the same piece throughout. Coverage measures the union of the current projected polygons; grey inserts are included. Red marks overlap. Airborne motion is not a tiling. Decorative thickness contributes no area.

Equations used in the module

Equations
a² + b² = c²  as area: the two leg squares cut and moved fill the hypotenuse square
Perigal: two perpendicular cuts through the centre of the b-square, four pieces + the a-square
the cuts come from the Pythagorean tiling of the plane
measured: covered area = c², no overlap

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