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A statistic which assigns a single number to several individual statistics in order to quantify trends. The best-known index in the United States is the consumer price index, ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

Let s=1/(sqrt(2pi))[Gamma(1/4)]^2=5.2441151086... (1) (OEIS A064853) be the arc length of a lemniscate with a=1. Then the lemniscate constant is the quantity L = 1/2s (2) = ...

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

The midsphere, also called the intersphere, reciprocating sphere, or inversion sphere, is a sphere with respect to which the polyhedron vertices of a polyhedron are the ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that S>=pi/2+2/pi=2.2074... (1) ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...