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The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Attach a string to a point on a curve. Extend the string so that it is tangent to the curve at the point of attachment. Then wind the string up, keeping it always taut. The ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

The function psi(x)={sin(x/c) |x|<cpi; 0 |x|>cpi, (1) which occurs in estimation theory.

Shapes such as segments or angles appear larger when placed inside a larger angle.

Each of the maps in a chain complex ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... is known as a boundary operator.

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

A dilation that is not merely a translation. Two triangles related by a central dilation are said to be perspective triangles because the lines joining corresponding vertices ...

Characteristic classes are cohomology classes in the base space of a vector bundle, defined through obstruction theory, which are (perhaps partial) obstructions to the ...

The space of continuously differentiable functions is denoted C^1, and corresponds to the k=1 case of a C-k function.