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Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

The polyhedron compound of the small rhombicuboctahedron and its dual, the deltoidal icositetrahedron. The compound can be constructed from a small rhombicuboctahedron of ...

Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

A geometric construction done with a movable compass alone. All constructions possible with a compass and straightedge are possible with a movable compass alone, as was ...

The Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...

A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the ...

The Euler-Gergonne-Soddy circle, a term coined here for the first time, is the circumcircle of the Euler-Gergonne-Soddy triangle. Since the Euler-Gergonne-Soddy triangle is a ...