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Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.

2 votes

Inside-out polygonal dissections

Riffing off the tiling comment to another answer, imagine a square penny packing of circles, and then translate the tiling so that a circle is in the center of four other circles. Now replace each of …
The Masked Avenger's user avatar
1 vote

Equipartition of the circle

Not quite an answer, but food for thought. Consider a curve with N (let's say distinct) distinguished points on it. Call two such C and D PR (or C PR D, for projectively related) if there is a point …
The Masked Avenger's user avatar