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Converted by Mathematica      November 6, 2002

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Euler created many standard mathematical notations. " ...... After his death in 1783 the St Petersburg Academy continued to publish Euler's unpublished work for nearly 50 more years.

Euler's work in mathematics is so vast that an article ... cannot but give a very superficial account of it. He was the most prolific writer of mathematics of all time. He made large bounds forward in the study of modern analytic geometry and trigonometry where he was the first to consider sin, cos etc. as functions rather than as chords as Ptolemy had done.

He made decisive and formative contributions to geometry, calculus and number theory. He integrated Leibniz's differential calculus and Newton's method of fluxions into mathematical analysis. He introduced beta and gamma functions, and integrating factors for differential equations. He studied continuum mechanics, lunar theory with Clairaut, the three body problem, elasticity, acoustics, the wave theory of light, hydraulics, and music. He laid the foundation of analytical mechanics, especially in his Theory of the Motions of Rigid Bodies (1765).

We owe to Euler the notation f(x) for a function (1734), e for the base of natural logs (1727), i for the square root of -1 (1777), p for pi, S for summation (1755), the notation for finite differences ... and many others. ..."*

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*September 1998, School of Mathematics and Statistics, University of St Andrews, Scotland,
http://www-history.mcs.st-andrews.ac.uk/history/References/Euler.html

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Hamming Distance
http://www.nist.gov/dads/HTML/hammingdist.html

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3n+1 or "Collatz" problem. Key reference: Jeff Lagarias, "The 3x + 1 Problem and Its Generalizations" American Mathematical Monthly 92-1, 1985, 3-23.

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http://www.cs.ucla.edu/~klinger/pami/simple_11_06_02.html

11/12/02 Version