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A number n for which a shortest chain exists (which is also a Hansen chain) is called a Hansen number.

The Harborth graph is the smallest known 4-regular matchstick graph. It is therefore both planar and unit-distance. It has 104 edges and 52 vertices. This graph was named ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...

The 6-polyiamond illustrated above.

A similarity transformation which preserves orientation, also called a homothety.

The 6-polyiamonds illustrated above.

100=10^2. Madachy (1979) gives a number of algebraic equations using the digits 1 to 9 which evaluate to 100, such as (7-5)^2+96+8-4-3-1 = 100 (1) 3^2+91+7+8-6-5-4 = 100 (2) ...

The Diophantine equation x_1^2+x_2^2+...+x_n^2=ax_1x_2...x_n which has no integer solutions for a>n.

A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...