Search Results for ""

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

The Chebyshev integral is given by intx^p(1-x)^qdx=B(x;1+p,1+q), where B(x;a,b) is an incomplete beta function.

int_a^bf_1(x)dxint_a^bf_2(x)dx...int_a^bf_n(x)dx <=(b-a)^(n-1)int_a^bf_1(x)f_2(x)...f_n(x)dx, where f_1, f_2, ..., f_n are nonnegative integrable functions on [a,b] which are ...

If a_1>=a_2>=...>=a_n (1) b_1>=b_2>=...>=b_n, (2) then nsum_(k=1)^na_kb_k>=(sum_(k=1)^na_k)(sum_(k=1)^nb_k). (3) This is true for any distribution.

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

The Chern number is defined in terms of the Chern class of a manifold as follows. For any collection Chern classes such that their cup product has the same dimension as the ...

The 6-polyiamond illustrated above.

Chinese checkers is a game roughly analogous to checkers played on a board in the shape of a centered hexagram. The board has a total of S_5=121 holes, where S_n is a star ...

An alternative term for a binomial coefficient, in which (n; k) is read as "n choose k." R. K. Guy suggested this pronunciation around 1950, when the notations ^nC_r and ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...