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Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...

The Jerabek hyperbola is a circumconic that is the isogonal conjugate of the Euler line (Kimberling 1998, p. 237). Since it is a circumconic passing through the orthocenter, ...

The Steiner deltoid is the envelope of the Simson lines of a triangle. Its circumcircle is the Steiner circle, and its incircle is the nine-point circle. The triangle formed ...

Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not. The term ...