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Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

The William Lowell Putnam Mathematics Competition is an annual mathematics contest open to North American college students administered by the Mathematical Association of ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

There are four fully supported stellations of the rhombic dodecahedron including as usual the original solid in the count (Wells 1991; Webb). The three nontrivial ones ...

A right angle is an angle equal to half the angle from one end of a line segment to the other. A right angle is pi/2 radians or 90 degrees. A triangle containing a right ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...