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Euler, Leonhard, 1707-83, Swiss mathematician. Born and educated at Basel, where he knew the Bernoullis, he went to St. Petersburg (1727) at the invitation of Catherine I, becoming professor of mathematics there on the departure of Daniel Bernoulli (1733). He was invited to Berlin (1741) by Frederick the Great and remained there until 1766, when he returned to St. Petersburg. Euler was the most prolific mathematician who ever lived; his collected works run to more than seventy volumes. He contributed to numerous areas of both pure and applied mathematics, including the calculus of variations, analysis, number theory, algebra, geometry, trigonometry, analytical mechanics, hydrodynamics, and the lunar theory (calculation of the motion of the moon). Euler was one of the first to develop the methods of the calculus on a wide scale. Though half-blind for much of his life and totally blind for the last seventeen years, he retained to the end a near-legendary skill at calculation. Among his results are the differential equation named for him, the formula relating the number of faces, edges, and vertices of a polyhedron (*F* + *V* = *E* + 2), and the famous equation *e*^{iπ} + 1 = 0 connecting five fundamental numbers in mathematics.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Frank, Leonhard, 1882-1961, German expressionist writer. He gained acclaim with his first novel, *The Robber Band* (1914, tr. 1928), and it was followed by such works as *The Cause of the Crime* (1920, tr. 1928), *A Middle*-*Class Man* (1924, tr. 1930), and *Carl and Anna* (1927, tr. 1929), his best-known novel, which he dramatized in 1929. *In the Last Coach* (1925, tr. 1935) is a volume of short stories. His writing is psychological in approach, antiwar, and shows a compassion for victims of an authoritarian society. Frank fled Germany in 1933 and did not return until after World War II.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

(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 ∑ for summation; ∫*math.n* for the sum of divisors of *math.n*; *math.e* for the base of the natural logarithm; *math.a*, *math.b*, and *math.c* for the sides of a triangle with *math.A*, *math.B*, and *math.C* for the opposite angles; *math.f*(*math.x*) for a function; π for the ratio of the circumference to the diameter of a circle; and *math.i* for

Learn more about Euler, Leonhard with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

(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 ∑ for summation; ∫*math.n* for the sum of divisors of *math.n*; *math.e* for the base of the natural logarithm; *math.a*, *math.b*, and *math.c* for the sides of a triangle with *math.A*, *math.B*, and *math.C* for the opposite angles; *math.f*(*math.x*) for a function; π for the ratio of the circumference to the diameter of a circle; and *math.i* for

Learn more about Euler, Leonhard with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Leonhard may refer to:

- Leonhard Euler (1707-1783), Swiss mathematician and physicist
- Leonhard Rauwolf (1535-1596), German physician and botanist
- Leonhard Hutter (1563-1616), German theologian
- Karl Leonhard (1904 - 1988), German psychiatrist

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Last updated on Thursday March 13, 2008 at 19:28:37 PDT (GMT -0700)

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Last updated on Thursday March 13, 2008 at 19:28:37 PDT (GMT -0700)

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