sandwiching a spline

The strong convex hull property says that for a spline of degree , the convex hull of at most control points of a spline contains the point of a spline at parameter . Intersection methods can use this property to rule out certain interections. Union of a convex hulls of consecutive points completely encompass the … More sandwiching a spline

Waist on a torus

Last year I worked on a interesting problem which asks about the possibility of partitioning a convex set in a plane in to internally disjoint convex pieces of equal area and perimeter. The problem has since been proved when is a prime power, by Aronov and Hubard and Roman Karasev for all dimensions. Here in … More Waist on a torus


The binomial like coefficients that we saw in earlier posts: are called –binomial coefficients. In keeping with the existing convention we will use as the indeterminate instead of and write for It was established in an earlier post that: Using this identity we may reduce the -binomial coefficient to: We also made use of the … More q-binomials