Abstract: The four-arcs method uses four arcs joining together similarly into an ellipse. Due to its
symmetry, we take a quater graphics as the researching object and solve the equations by using
dichotomy. Then we get the splicing point coordinates of the two pieces of circular arc. Then do error
analysis with the actual ellipse in the two pieces of circular arc, and list the mathematical equations of
the two pieces of circular arc and the ellipse polar. Then solve the actual maximum error value of the
ellipse and the two pieces of circular arc with Newton iterative method. After that, figure out the
approximate and actual ellipse areas, so as to work out the area error values. With the mathematical
model, the calculator software is developed. It is concluded that the error of the approximated ellipse is
solved through comparing the analysis list of calculating results.

Key words: ellipse, Newton iterative method, calculator, error analysis