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The compound of a truncated tetrahedron and its dual, the triakis tetrahedron. The compound can be constructed from a truncated octahedron of unit edge length by midpoint ...

A one-sided (singly infinite) Z-Transform, Z[{a_n}_(n=0)^infty](z)=sum_(n=0)^infty(a_n)/(z^n). This is the most common variety of Z-transform since it is essentially ...

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

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 roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...