# MPI-I-98-1-023

## Rational points on circles

### Burnikel, Christoph

**MPI-I-98-1-023**. October** **1998, 14 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

We solve the following problem.

For a given rational circle $C$ passing through the rational points

$p$, $q$, $r$ and a given angle $\alpha$, compute a rational point

on $C$ whose angle at $C$ differs from $\alpha$ by a value of

at most $\epsilon$.

In addition, try to minimize the bit length of the computed point.

This document contains the C++ program |rational_points_on_circle.c|.

We use the literate programming tool |noweb| by Norman Ramsey.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1998-1-023

**BibTeX**
`@TECHREPORT{``Burnikel98-1-023``,`

` AUTHOR = {Burnikel, Christoph},`

` TITLE = {Rational points on circles},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-98-1-023},`

` MONTH = {October},`

` YEAR = {1998},`

` ISSN = {0946-011X},`

`}`