# Introduction

- Author:
- Ku, Yin Bon (Albert)

After learning knowledge about constructible numbers in the last chapter, we are now ready to tackle the so-called "

**three classical problems**" in ancient Greek geometry. They are**Doubling a cube****Trisecting an angle****Squaring a circle**

**These problems were extremely influential in the development of Greek geometry. It turns out that none of the above can be done by Euclidean constructions. We will use the "****main theorem**" that will be introduced in the next page to prove that it is impossible to double a cube or trisect an angle by straightedge and compass only. As for squaring a circle, a more advanced theorem will be needed.