
The one-cut theorem: any polygon in a single cut | Tangente
The one-cut theorem
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.


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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Studying the geometric figures obtained by fully unfolding an origami creation has led to general theorems that can be stated simply. These results quickly lead to questions connected to major open problems in mathematics.

Some constructions impossible to achieve with straightedge and compass become possible using origami… but not all of them! Paper folding also lets us revisit several questions of concurrency or collinearity, and reflect on the construction of polygons.

Although Cauchy is widely regarded as a highly abstract thinker, the first chapter of his work is, by contrast, strikingly visual. His study of regular polyhedra marked his entry into the world of mathematical research.

Greek geometers regarded only straightedge-and-compass constructions as acceptable. Some problems that defeated their ingenuity—for reasons that would not be understood until the advent of algebra—can nevertheless be solved using origami.
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