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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 ...

A Pierpont prime is a prime number of the form p=2^k·3^l+1. The first few Pierpont primes are 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, ... ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

The coheight of a proper ideal I of a commutative Noetherian unit ring R is the Krull dimension of the quotient ring R/I. The coheight is related to the height of I by the ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

The study of designs and, in particular, necessary and sufficient conditions for the existence of a block design.