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An algebra with no nontrivial ideals.

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

The altitudes of a triangle are the Cevians A_iH_i that are perpendicular to the legs A_jA_k opposite A_i. The three altitudes of any triangle are concurrent at the ...

The antipedal triangle DeltaA^'B^'C^' of a reference triangle DeltaABC with respect to a given point P is the triangle of which DeltaABC is the pedal triangle with respect to ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

A polyhedron is said to be canonical if all its polyhedron edges touch a sphere and the center of gravity of their contact points is the center of that sphere. In other ...

If a discrete group of displacements in the plane has more than one center of rotation, then the only rotations that can occur are by 2, 3, 4, and 6. This can be shown as ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

The elongated square gyrobicupola nonuniform polyhedron obtained by rotating the bottom third of a small rhombicuboctahedron (Ball and Coxeter 1987, p. 137). It is also ...