DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## AD0270239

# Title:

## NUMERICAL EXPERIMENTS ON THE NUMBER OF LATTICE POINTS IN A CIRCLE

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

# Report Date:

## 1961-12-28

# Pagination or Media Count:

##
1.0

# 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, Ar denotes the number of lattice points of C and Er denotes the difference between Ar and one-half the circumference of C. Numerical information is considered for the functions Ar, Er, and Erthe 4th root of r. A method is devised for computing Ar 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 Ar is evaluated. Knowing Ar, approximate evaluations of Er and Erthe 4th root of r are readily obtained. The results of all computations are given in tabulated form.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#