Abstract: The study of pi is not only of interest to mathematicians and scientists, but also serves as the foundation for many problems
and applications in the fields of mathematics and science. This study constructed a projection model for estimating pi, which is based
on the Monte Carlo method and uses regular polygons circumscribed about a unit circle, and then improved the model. When the
number of experiments was 20 million, the accuracy of the model was compared and analyzed by using relative error, and was also
compared with that of the Buffon's needle experiment. The results showed that the accuracy of the projection model of the unit circle
circumscribed by an octagon was significantly better than that of the Buffon's needle experiment, with an estimated value of 3.141 59.
The results indicate that the model can effectively improve the accuracy of pi estimation.

Key words: Monte Carlo method, pi, Buffon's needle, relative error analysis