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Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same ...

A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...

An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

A figure resembling a daisy or sunflower in which copies of a geometric figure of increasing size are placed at regular intervals along a spiral. The resulting figure appears ...

The lituus is an Archimedean spiral with n=-2, having polar equation r^2theta=a^2. (1) Lituus means a "crook," in the sense of a bishop's crosier. The lituus curve originated ...

The problem of finding the strategy to guarantee reaching the boundary of a given region ("forest") in the shortest distance (i.e., a strategy having the best worst-case ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

A heterosquare is an n×n array of the integers from 1 to n^2 such that the rows, columns, and diagonals have different sums. (By contrast, in a magic square, they have the ...

Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if OP·OQ=k^2. If P describes a curve C_1, then Q describes a curve C_2 ...

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...