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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 Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...

A catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension ...

The maximum number of regions that can be created by n cuts using space division by planes, cube division by planes, cylinder cutting, etc., is given by N_(max)=1/6(n^3+5n+6) ...

A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes ...

A minimal surface given by the parametric equations x(u,v) = u-sinucoshv (1) y(u,v) = 1-cosucoshv (2) z(u,v) = 4sin(1/2u)sinh(1/2v) (3) (Gray 1997), or x(r,phi) = ...

Given A = |a_(11)-x a_(12) ... a_(1m); a_(21) a_(22)-x ... a_(2m); | | ... |; a_(m1) a_(m2) ... a_(mm)-x| (1) = x^m+c_(m-1)x^(m-1)+...+c_0, (2) then ...

A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper ...

A chamfered cube, also inaccurately called a truncated rhombic dodecahedron or more accurately called a tetratruncated rhombic dodecahedron, is a polyhedron obtained by ...

A chamfered octahedron, which could also know known as a tritruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a regular octahedron. The illustration ...