Search Results for ""

Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same ...

"Q.E.D." (sometimes written "QED") is an abbreviation for the Latin phrase "quod erat demonstrandum" ("that which was to be demonstrated"), a notation which is often placed ...

Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

The 9.1.2 equation A^9=B^9+C^9 (1) is a special case of Fermat's last theorem with n=9, and so has no solution. No 9.1.3, 9.1.4, 9.1.5, 9.1.6, 9.1.7, 9.1.8, or 9.1.9 ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

The Dottie number is the name given by Kaplan (2007) to the unique real root of cosx=x (namely, the unique real fixed point of the cosine function), which is 0.739085... ...