Three Problems of Antiquity

All our geometry, whether limited to circles and. straight lines or extended to include conic sections and higher plane curves, had its origin solely in Greek civilization. Geometry has gone through many different stages, beginning with geometric forms. It was out of this interest in geometric forms and their construction that the three\u27 problems of antiquity, the trisection of an angle, the quadrature of a circle, and the duplication of a cube, evolved. In my paper I dealt with each- of these three problems in detail. First, I demonstrated the impossibility of their solution by the use of straightedge and compass alone. Developing each problem further, I discussed Greek geometers who used means other than Euclidean tools to try and solve them. Lastly, I expounded on their constructions, either proving them or pointing out the fallacy in their methods. The men whose material I expounded upon are by no means the only ones who worked on the solution of these problems. However, I chose to discuss their methods because I found them interesting as well as unique