Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree $10$ rather than $6$; the Chebyshev error function equioscillates $11$ times rather than $7$; the approximation order is $10$ rather than $6$. The method approximates more than the full circle with Chebyshev uniform error of $1/2^{9}$. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.
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Jordan University of Science and Technology
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