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Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

At the points where a line X cuts the sides of a triangle DeltaA_1A_2A_3, draw three perpendiculars to the sides, one through each point of intersection. The resulting three ...

The perpendicular foot, also called the foot of an altitude, is the point on the leg opposite a given vertex of a triangle at which the perpendicular passing through that ...

A pivotal isocubic is an isocubic on the lines connecting pairs of isoconjugates that pass through a fixed point P (the pivot point). Pivotal isocubics intersect the ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

Two triangles are said to be poristic triangles if they share the same incircle and circumcircle. More specifically, in the plane of a reference triangle, a triangle is said ...

A primitive Pythagorean triple is a Pythagorean triple (a,b,c) such that GCD(a,b,c)=1, where GCD is the greatest common divisor. A right triangle whose side lengths give a ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...

A self-isogonal cubic us a triangle cubic that is invariant under isogonal conjugation. The term is commonly applied to mean a pivotal isogonal cubic, in which points P lying ...

A self-isotomic cubic us a triangle cubic that is invariant under isotomic conjugation. The term is commonly applied to mean a pivotal isotomic cubic, in which points P lying ...