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A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...

In one dimension, the interval [0,1] is the closed unit interval, the interval (0,1) is the open unit interval, and the intervals (0,1] and [0,1) are half-open unit intervals.

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...