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The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem. It was also investigated by Steiner ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...