Leonhard Euler summary

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Leonhard Euler, (born April 15, 1707, Basel, Switz.—died Sept. 18, 1783, St. Petersburg, Russia), Swiss mathematician. In 1733 he succeeded Daniel Bernoulli (see Bernoulli family) at the St. Petersburg Academy of Sciences. There he developed the theory of trigonometric and logarithmic functions and advanced mathematics generally. Under the patronage of Frederick the Great, he worked at the Berlin Academy for many years (1744–66), where he developed the concept of function in mathematical analysis and discovered the imaginary logarithms of negative numbers. Throughout his life he was interested in number theory. In addition to inspiring the use of arithmetic terms in writing mathematics and physics, Euler introduced many symbols that became standard, including Σ for summation; ∫n for the sum of divisors of n; e for the base of the natural logarithm; a, b, and c for the sides of a triangle with A, B, and C for the opposite angles; f(x) for a function; π for the ratio of the circumference to the diameter of a circle; and i for Square root of√−1. He is considered one of the greatest mathematicians of all time.

An illustration of the difference between average and instantaneous rates of changeThe graph of f(t) shows the secant between (t, f(t)) and (t + h, f(t + h)) and the tangent to f(t) at t. As the time interval h approaches zero, the secant (average speed) approaches the tangent (actual, or instantaneous, speed) at (t, f(t)).

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