Can a polygon be cut from a sheet of paper with a single straight cut? Surprisingly, the answer is yes! More surprisingly still, this also applies to other objects.
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One of the arts and pleasures of mathematics is finding different ways to represent problems. Some problems in dynamics can profitably be replaced by the study of trajectories on a billiard table, revealing hidden structures—and hence hidden logical beauty.
The concept of measurement evolved over a long period, from concrete practice to abstraction, in a process initiated by Archimedes. This required mastering the concept of infinity.
Popularized by Martin Gardner, flexagons are geometric curiosities that sparked huge enthusiasm among the general public. Although their mathematical study began in the 1940s, they have not yet given up all their secrets.
A symmetry appearing out of nowhere, an equilateral triangle emerging amid the trisectors of a completely arbitrary triangle: that is the whole "miracle" of Morley and his theorem. The many proofs of this beautiful property are marvels of geometry and trigonometry.
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