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Every convex body B in the Euclidean plane with area A can be inscribed in a triangle of area at most equal to 2A (Gross 1918, Eggleston 1957). The worst possible fit ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

Whirls are figures constructed by nesting a sequence of polygons (each having the same number of sides), each slightly smaller and rotated relative to the previous one. The ...

The ordinary differential equation y=xf(y^')+g(y^'), where y^'=dy/dx and f and g are given functions. This equation is sometimes also known as Lagrange's equation (Zwillinger ...

The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

The likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...

The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). The first few values are 1, 0, ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...