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At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

The largest area of intersection of a solid body by a plane parallel to a given plane, also called the "HA measurement."

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A=pir_A^2) with same perimeter (p=2pir_p) as the curve, Q = ...

A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single ...

The Jordan canonical form, also called the classical canonical form, of a special type of block matrix in which each block consists of Jordan blocks with possibly differing ...

An algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It is an algorithm which makes optimal use of imprecise data on a linear (or ...

The thinnest sequence which contains 1, and whenever it contains x, also contains 2x, 3x+2, and 6x+3: 1, 2, 4, 5, 8, 9, 10, 14, 15, 16, 17, ... (OEIS A005658).

The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...