ABSTRACT
Abraham de Moivre is famous for his formula ( cos x + i sin x ) n = cos ( n x ) + i sin ( n x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315069555/5d5201a7-70ac-4d14-a96d-80b2cf916e2e/content/eqn0021.tif"/> which had profound effects on the uses of trigonometry in mathematics. This formula is also linked to one of the most beautiful formulas in mathematics, e π i + 1 = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315069555/5d5201a7-70ac-4d14-a96d-80b2cf916e2e/content/ieq0035.tif"/> , which links the five most important constants in mathematics. These are 0, 1, e =2.718 281… (see chapter E), π = 3.141592 Chapter P) and i = − 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315069555/5d5201a7-70ac-4d14-a96d-80b2cf916e2e/content/ieq0036.tif"/> . Why are these five seemingly unrelated fundamental numbers linked in one equation? Professor Feynman, the Nobel prize-winning physicist, states that this is one of the most remarkable formulas known to man; he says ‘it is a jewel’.
