After learning knowledge about constructible numbers in the last chapter, we are now ready to tackle the so-called "[b][color=#0000ff]three classical problems[/color][/b]" in ancient Greek geometry.  They are[br][br][list][*][color=#0000ff][b][/b][b]Doubling a cube[/b][/color][/*][*][color=#0000ff][b][/b][b]Trisecting an angle[/b][/color][/*][*][color=#0000ff][b][/b][b]Squaring a circle[/b][/color][/*][/list][b][br][/b]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 "[b][color=#0000ff]main theorem[/color][/b]" 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.