Abstract: The distance of equidistant curves is used to estimate the errors between an ellipse
and the four-arcs which approximate the ellipse. An explicit expression of the errors and the
semi-axes of the ellipse are established. A new method is proposed for approximating an ellipse by
using of four-arcs with minimal error via symbolic computation and regression analysis. Our
method is easy for drawing with ruler and compass and can be used in interpolation programming
for the computerized Numerical Control lathes.

Key words: four-arcs, error analysis, ellipse, equidistant curve