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The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

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 Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

A set A of integers is said to be one-one reducible to a set B (A<<_1B) if there is a one-one recursive function f such that for every x, x in A=>f(x) in B (1) and f(x) in ...

A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable forms which cannot be continuously ...

A Fourier series-like expansion of a twice continuously differentiable function f(x)=1/2a_0+sum_(n=1)^inftya_nJ_0(nx) (1) for 0<x<pi, where J_0(x) is a zeroth order Bessel ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

The small ditrigonal icosidodecahedron is the uniform polyhedron with Maeder index 30 (Maeder 1997), Weinninger index 70 (Wenninger 1971, p. 106-107), Coxeter index 39 ...