How Does Topology Help Solve the Inscribed Rectangle Problem by Proving that Every Jordan Curve Has 4 Vertices that Form a Rectangle?

Computing the largest inscribed isothetic rectangle

This paper describes an algorithm to compute, in (log n) time, a rectangle that is contained in a convex n-gon, has sides parallel to the coordinate axes, and has maximum area. With a slight modiication it will compute the smallest perimeter. The algorithm uses a tentative prune-and-search approach, even though this problem does not appear to t into the functional framework of Kirkpatrick and S...

Algorithm for finding the largest inscribed rectangle in polygon

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

Enumeration of polyominoes inscribed in a rectangle

Proving that a genus 2 curve has complex multiplication

Recently examples of genus 2 curves defined over the rationals were found which, conjecturally, should have complex multiplication. We prove this conjecture. This involves computing an explicit representation of a rational map defining complex multiplication.

The Runaway Rectangle Escape Problem

Motivated by the applications of routing in PCB buses, the Rectangle Escape Problem was recently introduced and studied. In this problem, we are given a set of rectangles S in a rectangular region R, and we would like to extend these rectangles to one of the four sides of R. Define the density of a point p in R as the number of extended rectangles that contain p. The question is then to find an...