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On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n-k)-forms. If w is an ...

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

A hyperbolic version of the Euclidean icosahedron.

The roulette of the pole of a hyperbolic spiral rolling on a straight line is a tractrix.

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 ...

A d-hyperoctant is one of the 2^d regions of space defined by the 2^d possible combinations of signs (+/-,+/-,...,+/-). The 2-hyperoctant is known as a quadrant and the ...

The term "ill-defined" is also used informally to mean ambiguous.

The imaginary number i=sqrt(-1), i.e., the square root of -1. The imaginary unit is denoted and commonly referred to as "i." Although there are two possible square roots of ...

Three impossible ways to combine four bars.

An impossible figure that locally (but only locally!) looks like a torus.