Search Results for ""

The motivating force of topology, consisting of the study of smooth (differentiable) manifolds. Differential topology deals with nonmetrical notions of manifolds, while ...

A multiplication * is said to be right distributive if (x+y)z=xz+yz for every x, y, and z. Similarly, it is said to be left distributive if z(x+y)=zx+zy for every x, y, and ...

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with ...

Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin(2x) = 2sinxcosx (1) cos(2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = ...

A hendecagon is an 11-sided polygon, also variously known as an undecagon or unidecagon. The term "hendecagon" is preferable to the other two since it uses the Greek prefix ...

A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the ...

Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

Two events A and B are called independent if their probabilities satisfy P(AB)=P(A)P(B) (Papoulis 1984, p. 40).

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...