Converted by Mathematica
November 6, 2002
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unpublished work for nearly 50 more years.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. ..."*
*September 1998, School of Mathematics and Statistics,
University of St Andrews, Scotland,
http://www-history.mcs.st-andrews.ac.uk/history/References/Euler.html
Hamming
Distance
http://www.nist.gov/dads/HTML/hammingdist.html
3n+1 or "Collatz" problem. Key reference: Jeff Lagarias, "The 3x + 1
Problem and Its Generalizations" American
Mathematical Monthly 92-1, 1985, 3-23.