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A rose curve, also called Grandi's rose or the multifolium, is a curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

A base-b BBP-type formula is a convergent series formula of the type alpha=sum_(k=0)^infty(p(k))/(b^kq(k)) (1) where p(k) and q(k) are integer polynomials in k (Bailey 2000; ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...