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The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope. It is a regular polytope with mutually perpendicular sides, and is ...

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles. The Malfatti configuration ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

A Mersenne number is a number of the form M_n=2^n-1, (1) where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first ...

A Mrs. Perkins's quilt is a dissection of a square of side n into a number of smaller squares. The name "Mrs. Perkins's Quilt" comes from a problem in one of Dudeney's books, ...

A game played on a board of a given shape consisting of a number of holes of which all but one are initially filled with pegs. The goal is to remove all pegs but one by ...

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...