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For a given monic quartic equation f(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0, (1) the resolvent cubic is the monic cubic polynomial g(x)=x^3+b_2x^2+b_1x+b_0, (2) where the coefficients ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

In the illusion illustrated above, when the concentric square borders with rounded edges are rotated slowly, the entire pattern appears to pulsate radially.

A Greek cross rotated by 45 degrees, also called the crux decussata, illustrated schematically above in polyomino form. The multiplication sign × is based on Saint Andrew's ...

A sorting method proposed by Shell (1959) in which records being sorted can take long jumps instead of being restricted to short steps.

A relationship between knot polynomials for links in different orientations (denoted below as L_+, L_0, and L_-). J. H. Conway was the first to realize that the Alexander ...

If {a_0,a_1,...} is a recursive sequence, then the set of all k such that a_k=0 is the union of a finite (possibly empty) set and a finite number (possibly zero) of full ...

The dual polyhedron of the small dodecahemicosahedron U_(62) and Wenninger dual W_(100). When rendered, the small dodecahemicosacron and great dodecahemicosacron appear the ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

The image on the Riemann sphere of any circle under a complex rational mapping with numerator and denominator having degrees no more than n has length no longer than 2npi.