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The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

The "witch of Agnesi" is a curve studied by Maria Agnesi in 1748 in her book Instituzioni analitiche ad uso della gioventù italiana (the first surviving mathematical work ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...

The isotomic conjugate of a point is the point of concurrence Q of the isotomic lines relative to a point P. The isotomic conjugate alpha^':beta^':gamma^' of a point with ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...