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

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

The third Brocard point has triangle center function alpha=a^(-3) and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its ...

Brocard's conjecture states that pi(p_(n+1)^2)-pi(p_n^2)>=4 for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few ...

The second Brocard Cevian triangle is the Cevian triangle of the second Brocard point. It has area Delta_2=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

The Tucker-Brocard cubic is the triangle cubic with trilinear equation abcsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2)=alphabetagammasum_(cyclic)a^2(b^4+c^4). It passes through ...

Lemoine geometry is that part of triangle geometry concerned with symmedians and symmedian points.

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...