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Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

The Parry point is one of the two intersections of the Parry circle and the circumcircle of a triangle (the other is the focus of the Kiepert parabola, which is Kimberling ...

Let L, M, and N be lines through A, B, C, respectively, parallel to the Euler line. Let L^' be the reflection of L in sideline BC, let M^' be the reflection of M in sideline ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

The pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(31). The unit pentagonal gyrobicupola has volume V=1/3(5+4sqrt(5)) (1) and Dehn invariant D ...

The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30). The unit pentagonal ...

The pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower faces arranged symmetrically about the midplane. It is Johnson ...

The pentagonal orthocupolarotunda is a convex equilateral solid that is Johnson solid J_(32). The unit pentagonal orthocupolarotunda has volume V=1/3(5+4sqrt(5)) (1) and Dehn ...