There is a famous formula, perhaps the most compact and famous of all formulas developed by Euler from a discovery of de Moivre: It appeals equally to the mystic, the scientist, the philosopher, the mathematician.
As Eisenstein shows, his method for constructing elliptic functions applies beautifully to the simpler case of trigonometric functions. Moreover, this case provides not merely an illuminating introduction to his theory, but also the simplest proofs for a series of results, originally discussed by Euler.ferdinand eisenstein
Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.william poundstone
Je voulus faire un jet d’eau dans mon jardin; Euler calcula l’effort des roues pour faire monter l’eau dans un bassin, d’où elle devait retomber par des canaux, afin de jaillir à Sans-Souci. Mon moulin a été exécuté géométriquement, et il n’a pu élever une goutte d’eau à cinquante pas du bassin. Vanité des vanités! vanité de la géométrie!Frederick II of Prussia
One of the most frequently mentioned equations was Euler 's equation, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty "; and " mind -blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing ?" The equation contains nine basic concepts of mathematics once and only once in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.
There is a famous formula, perhaps the most compact and famous of all formulas developed by Euler from a discovery of de Moivre: It appeals equally to the mystic , the scientist , the philosopher , the mathematician .
Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!