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The half-altitude circle is the circumcircle of the half-altitude triangle. The circle function is given by l=(f(a,b,c))/(128a^2b^3c^3cosAcosBcosC), (1) where (2) which is ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...

A congruent number can be defined as an integer that is equal to the area of a rational right triangle (Koblitz 1993). Numbers (a,x,y,z,t) such that {x^2+ay^2=z^2; ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its ...

A description of an object by properties that are different from those mentioned in its definition, but are equivalent to them. The following list gives a number of examples. ...

The quantity ps-rq obtained by letting x = pX+qY (1) y = rX+sY (2) in ax^2+2bxy+cy^2 (3) so that A = ap^2+2bpr+cr^2 (4) B = apq+b(ps+qr)+crs (5) C = aq^2+2bqs+cs^2 (6) and ...