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Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...

The recursive sequence defined by the recurrence relation a(n)=a(a(n-1))+a(n-a(n-1)) (1) with a(1)=a(2)=1. The first few values are 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, ... (OEIS ...

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance to a schematic illustration of a house ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

A regularly spaced array of points in a square array, i.e., points with coordinates (m,n,...), where m, n, ... are integers. Such an array is often called a grid or mesh, and ...

Interval arithmetic is the arithmetic of quantities that lie within specified ranges (i.e., intervals) instead of having definite known values. Interval arithmetic can be ...

The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p. 892). Each diagonal ...

Jacobi's imaginary transformations relate elliptic functions to other elliptic functions of the same type but having different arguments. In the case of the Jacobi elliptic ...