Folding rulers inside triangles

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چکیده

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Folding Rulers inside Triangles

An l-ruler is a chain of n links, each of length l. The links, which are allowed to cross, are modelled by line segments whose endpoints act as joints. A given connguration of an l-ruler is said to fold if it can be moved to a connguration in which all its links coincide. We show that l-rulers connned inside an equilateral triangle of side 1 exhibit the following surprising alternation property...

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Spherical and planar folding tessellations by kites and equilateral triangles

We prove that there is a unique folding tessellation of the sphere and an infinite family of folding tessellations of the plane with prototiles a kite and an equilateral triangle. Each tiling of this family is obtained by successive gluing of two patterns composed of triangles and kites, respectively. The combinatorial structure and the symmetry group is achieved.

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ژورنال

عنوان ژورنال: Discrete & Computational Geometry

سال: 1996

ISSN: 0179-5376,1432-0444

DOI: 10.1007/bf02711495