NUMERICAL EXPERIMENTS ON THE NUMBER OF LATTICE POINTS IN A CIRCLE
Abstract
A lattice point is any point in the plane having integer Cartesian coordinates. If C is a circle in the plane, the lattice points of C are those lattice points on the boundary or in the interior of C. If C is a circle of radius (square root of r), and if C is centered at (0,0), A(r) denotes the number of lattice points of C and E(r) denotes the difference between A(r) and one-half the circumference of C. Numerical information is considered for the functions A(r), E(r), and E(r)/(the 4th root of r). A method is devised for computing A(r) on a digital computer for all values of r which are perfect squares in the closed interval (1,4 time 10 to the 10th power). The method is then utilized in a computer program, and A(r) is evaluated. Knowing A(r), approximate evaluations of E(r) and E(r)/(the 4th root of r) are readily obtained. The results of all computations are given in tabulated form.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 28, 1961
- Accession Number
- AD0270239
Entities
People
- Harry Lawrence Mitchell
Organizations
- Stanford University