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Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

The expansion of the two sides of a sum equality in terms of polynomials in x^m and y^k, followed by closed form summation in terms of x and y. For an example of the ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

A sphericon is the solid formed from a bicone with opening angle of 90 degrees (and therefore with a=r=h) obtained by slicing the solid with a plane containing the rotational ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c<a. The exterior surface is called an apple ...

The Lie derivative of a spinor psi is defined by L_Xpsi(x)=lim_(t->0)(psi^~_t(x)-psi(x))/t, where psi^~_t is the image of psi by a one-parameter group of isometries with X ...

The equation of the curve of intersection of a torus with a plane perpendicular to both the midplane of the torus and to the plane x=0. (The general intersection of a torus ...

A hypotrochoid generated by a fixed point on a circle rolling inside a fixed circle. The curves above correspond to values of a=0.1, 0.2, ..., 1.0. Additional attractive ...

A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...

Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can ...