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A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every pair of faces has a polygon edge in common. The Szilassi polyhedron ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...

A figurate number of the form 4n^2-3n. The first few are 1, 10, 27, 52, 85, ... (OEIS A001107). The generating function giving the decagonal numbers is ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...