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A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

Rule 188 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Suppose that f is an analytic function which is defined in the upper half-disk {|z|^2<1,I[z]>0}. Further suppose that f extends to a continuous function on the real axis, and ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

A special type of binary tree obtained by starting with the fractions 0/1 and 1/0 and iteratively inserting (m+m^')/(n+n^') between each two adjacent fractions m/n and ...

Synergetics coordinates are a set of triangular coordinates in their plane (or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions). ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...