Search Results for ""

Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...