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If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).
The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...
A long division in which most or all of the digits are replaced by a symbol (usually asterisks) to form a cryptarithmetic.
A congruence that has a solution.
The continuous image of a Polish space, also called an analytic set.
Denoted sl_n.
The word "spectrum" confusingly has a number of unrelated meanings in various branches of mathematics.
The scalar |v|=ds/dt, where s is the arc length, equal to the magnitude of the velocity v.
A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...
There are 14 families of spherical groups, which can be written in orbifold notation as *532, 532, *432, 432, *332, 3*2, 332, *22N, 2*N, 22N, *NN, N*, Nx, and NN.
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