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Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...

A homographic transformation x_1 = (ax+by+c)/(a^('')x+b^('')y+c^('')) (1) y_1 = (a^'x+b^'y+c^')/(a^('')x+b^('')y+c^('')) (2) with t_1 substituted for t according to ...

A polyhex consisting of hexagons arranged along a line.

If there is an integer x such that x^4=q (mod p), then q is said to be a biquadratic residue (mod p). If not, q is said to be a biquadratic nonresidue (mod p).

A capsule is a term coined here for a stadium of revolution, i.e., a cylinder with two hemispherical caps on either end. The capsule is implemented in the Wolfram Language as ...

A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The ith Chern class is an obstruction to the ...

A typesetting symbol which has several distinct meanings in mathematics. It is used for a number of purposes. 1. To denote Boundaries between elements in a list, as in ...

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

A fractal curve of infinite length which bounds an area twice that of the original square.

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...