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The paradox "This statement is false," stated in the fourth century BC. It is a sharper version of the Epimenides paradox, "All Cretans are liars...One of their own poets has ...

The sequence defined by H(0)=0 and H(n)=n-H(H(H(n-1))). The first few terms are 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, ... (OEIS A005374).

A system in which a strange loop appears.

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

The meeting point of lines that connect corresponding points from homothetic figures. In the above figure, O is the homothetic center of the homothetic figures ABCDE and ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

The number of degrees of freedom in a problem, distribution, etc., is the number of parameters which may be independently varied.

The number q in a fraction p/q.

n sets of s trials each, with the probability of success p constant in each set. var(x/n)=spq+s(s-1)sigma_p^2, where sigma_p^2 is the variance of p_i.