Abstract
This chapter presents a few irrational numbers. Irrational numbers, the numbers which are not the ratio of two integers, has been known for a very long time. The Greeks were both well aware of this fact and extremely mystified by it. They were accustomed to think of geometry as the basic mathematical and scientific activity. They used numbers principally to describe geometrical situations and introduced algebraic operations on numbers because they needed them in evaluating their geometrical concepts. To them a number was essentially the length of a segment. Their geometry was based upon constructions using only a pair of compasses and a ruler. With these simple tools and with much ingenuity, they constructed proofs of theorems that even today are regarded as the models of elegance. On the whole, these constructions were adequate for their needs, but they were hindered by their inability to develop the numerical concepts needed to explain their geometrical constructions.
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