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The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A well-formed formula B is said to be true for the interpretation M (written |=_MB) iff every sequence in Sigma (the set of all denumerable sequences of elements of the ...

The base 8 notational system for representing real numbers. The digits used are 0, 1, 2, 3, 4, 5, 6, and 7, so that 8_(10) (8 in base 10) is represented as 10_8 ...

If a number fails Miller's primality test for some base a, it is not a prime. If the number passes, it may be a prime. A composite number passing Miller's test is called a ...

Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive ...