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Characteristic classes are cohomology classes in the base space of a vector bundle, defined through obstruction theory, which are (perhaps partial) obstructions to the ...

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy |l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 ...

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

A pair of conics obtained by expanding an equation in Monge's form z=F(x,y) in a Maclaurin series z = z(0,0)+z_1x+z_2y+1/2(z_(11)x^2+2z_(12)xy+z_(22)y^2)+... (1) = ...

Given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by e={sqrt((a^2-c^2)/(a^2)) c<a (oblate spheroid); sqrt((c^2-a^2)/(c^2)) c>a (prolate ...