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Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

A Julia set with c=-0.123+0.745i, also known as the dragon fractal.

If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf. Renteln and Dundes (2005) ...

An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

A Maurer rose is a plot of a "walk" along an n- (or 2n-) leafed rose curve in steps of a fixed number d degrees, including all cosets.

A beautiful class of polyhedra composed of rhombic faces discovered accidentally by R. Towle while attempting to develop a function to create a rhombic hexahedron from a ...

Sparklines are word-like graphics that have an intensity of visual distinctions comparable to words or letters (Tufte 2006, p. 4).

A sphere with three handles (and three holes), i.e., a genus-3 torus.