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A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

Let a tree S be a subgraph of a cubic graph G. The graph excision G circleminus S is the graph resulting from removing the tree, then merging the edges. For example, if in ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

A quasiregular polyhedron is the solid region interior to two dual regular polyhedra with Schläfli symbols {p,q} and {q,p}. Quasiregular polyhedra are denoted using a ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

A 15-sided polygon, sometimes also called the pentakaidecagon. For a regular pentadecagon with side length 1, the inradius r, circumradius R, and area A are r = ...

A 30-sided polygon. The regular triacontagon with side length 1 has inradius r, circumradius R, and area A given by r = 1/4(sqrt(15)+3sqrt(3)+sqrt(2)sqrt(25+11sqrt(5))) (1) R ...

A 24-sided polygon. The regular icositetragon is constructible. For side length 1, the inradius r, circumradius R, and area A are given by r = 1/2(2+sqrt(2)+sqrt(3)+sqrt(6)) ...