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To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

Let a triangle have angles A, B, and C, then inequalities include sinA+sinB+sinC<=3/2sqrt(3) (1) 1<=cosA+cosB+cosC<=3/2 (2) sin(1/2A)sin(1/2B)sin(1/2C)<=1/8 (3) ...

The sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

The triangular cupola is Johnson solid J_3. Its faces consist of 4 equilateral triangles, 3 squares, and 1 hexagon. It is implemented in the Wolfram Language as ...

The triangular (or trigonal) dipyramid is one of the convex deltahedra, and Johnson solid J_(12). It is also an isohedron. It is implemented in the Wolfram Language as ...

A triangular grid, also called an isometric grid (Gardner 1986, pp. 209-210), is a grid formed by tiling the plane regularly with equilateral triangles.

Johnson solid J_(92).

The triangular inequalities are the inequalities |x-y|<=z<=x+y for real numbers (x,y,z) (Messiah 1962, p. 1056). If these inequalities hold for any one permutation of ...