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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.

The even impulse pair is the Fourier transform of cos(pik), AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2). (1) It ...

A disjunction that remains true if either or both of its arguments are true. This is equivalent to the OR connective. By contrast, the exclusive disjunction is true if only ...

Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies P(A|B)=P(A), (1) in which case the probability of A and B is ...