Abstract: Recursion formula is generated and proved in connection with the calculation of vertex coordinates of a regular polygon. Based on the new formula, the algorithm for generating regular polygon and circle is put forward, whose error analysis is given. The calculation of every vertex of a regular polygon calls for multiplication and addition twice respectively. The new method is better than that of polygon approximation. The algorithm is of the characteristics of simple construction, fast execution speed and high accuracy.

Key words: circle, algorithm, polygon approximation, error analysis