*Gale*. ©2005-2006 Thomson Gale, a part of the Thomson Corporation. All rights reserved.

This section contains 1,483 words(approx. 5 pages at 300 words per page) |

*World of Mathematics* on Leonhard Euler

Leonhard Euler advanced every known field of mathematics in his day. A prolific author, among his greatest writings are treatises on **analytic geometry**, differential and integral **calculus**, and the calculusof variations. Euler developed spherical **trigonometry**, demonstrated the importance of **convergence** in algebraic series, proved important assertions in **number theory**, and made contributions to **hydrodynamics**, celestial **mechanics**, and optics. Euler also brought into common usage such mathematical notations "e" for the base of the natural logarithm, "i" for the **square** root of negative 1, and *f*(x) for a function of x. A variety of mathematical concepts bear his name, including Euler's characteristicin **topology**, Euler's trianglein **geometry**, Euler's **polynomials**, Euler's integrals, and Euler's constant. His accomplishments are especially remarkable in that many were made during the last quarter of his life, when he was totally blind.

Euler was born in Basel, Switzerland, on April 17, 1707 to Paul Euler and Marguerite Brucker...

This section contains 1,483 words(approx. 5 pages at 300 words per page) |