Conclusion

The three ancient construction problems of squaring the circle, trisecting the angle, and doubling the cube have puzzled mathematicians and amateurs since the days of ancient Greece. Accurate approximations to the solution have been constructed, and if methods other than compass and straightedge constructions are allowed, exact constructions can also be created. After many attempts at solving the problem by many different mathematicians, Lindemann proved in 1880 that it is impossible to square the circle using a compass and straightedge.