Rational points on circles

Burnikel, Christoph

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Rational points on circles

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Burnikel, Christoph
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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1998-1-023
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Burnikel, C.(1998). Rational points on circles (MPI-I-1998-1-023). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-7B72-E

Abstract

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.