ABSTRACT
Geometry is one of the oldest branches of mathematics, said to be invented by the ancient Egyptians to help them draw maps of their fields flooded by the river Nile every year. It was then perfected by the Greek philosophers who added axioms, proofs and constructions to the subject. Euclid's book, The Elements of Geometry, is one of the best-selling books of all time and set standards of logic and deduction that have greatly influenced the development of human thought, as well as construction, engineering and science. Many geometric proofs were almost purely lateral, long before the term was in common usage.
This chapter has many problems about common geometric shapes encountered in everyday life – straight lines, triangles, circles, semicircles, ellipses, hexagons and cubes. The famous number phi, the golden ratio, arises too in a novel setting.
The great French mathematician Rene Descartes revolutionized mathematics with an astonishingly lateral technique of effectively turning geometry into algebra. He discovered that geometric shapes could be represented by algebraic equations. For example, all properties of a circle can be deduced from the equation x^2 + y^2 = 1. Many of the geometric problems in this chapter can be solved laterally by translating them into algebraic language.
