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Given a regular tetrahedron of unit volume, the mean triangle area of a triangle picked at random inside it is approximately A=0.1811+/-0.0012, and the variance is ...

The dual polyhedron of the tetrahemihexahedron U_4 and Wenninger dual W_(67).

Lachlan's term for a set of four points, no three of which are collinear.

An inscribed angle in a semicircle is a right angle.

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

The third Brocard triangle is Gibert's term for the isogonal conjugate of the first Brocard triangle. It has trilinear vertex matrix [b^2c^2 ab^3 ac^3; a^3b a^2c^2 bc^3; a^3c ...

The third Lemoine circle, a term coined here for the first time, is the circumcircle of the Lemoine triangle. It has center function alpha=(f(a,b,c))/a, (1) where f(a,b,c) is ...

The third mid-arc point is the triangle center with triangle center function alpha_(2089)=[-cos(1/2A)+cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(2089).

The third Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-4pi)] sec[1/3(B-4pi)]; sec[1/3(C-4pi)] 2 sec[1/3(A-4pi)]; sec[1/3(B-4pi)] sec[1/3(A-4pi)] 2]. The ...

The third Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 357, 358, 1136, and 1137.