Galois theory - Ian Stewart (Chapman and Hall, 1998)
The book is a showpiece of mathematical unification and "technology transfer". Abstract algebraic techniques, such as group theory and field theory, are used to answer important questions in geometry and the theory of equations. These applications include the impossibility of trisecting the angle, duplicating the cube, squaring the circle or solving equations of the fifth degree. They also include the possibility of constructing regular polygons with 17,257 and 65,735 sides. There are over 200 exercises, including hints and a selection of solutions