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Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

The region lying between two concentric circles. The area of the annulus formed by two circles of radii a and b (with a>b) is A_(annulus)=pi(a^2-b^2). The annulus is ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

The bigyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(79). The unit bigyrate diminished rhombicosidodecahedron has volume ...

A coordinate system obtained by inversion of the bicyclide coordinates. They are given by the transformation equations x = Lambda/(aUpsilon)snmudnnucospsi (1) y = ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...