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Transcript of Leonhard Euler
.Modern mathematics owes a great deal to the efforts of Leonhard Euler. Not only did he make enormous strides in the study of advanced mathematics
.He was the first to establish a consistency with the use of letters of the alphabet
. Lowercase letters represented the sides of a triangle and uppercase letters represented the opposite angles. He standardized the use of the letter e to represent the base system of natural logarithms
. He was also the first to use circles to show the relationship of sets, but instead of calling them Euler Circles, they are identified as Venn Diagrams
Euler also discovered the formula V − E + F = 2 relating the number of vertices, edges and faces of a convex polyhedron,[
The constant in this formula is now known as the Euler characteristic for the graph (or other mathematical object)
In 1735, Euler presented a solution to the problem known as the Seven Bridges of Königsberg
The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point.
.A lot of Euler's early work on number theory was based on the works of Pierre de Fermat.
. Euler proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and he made distinct contributions to Lagrange's four-square theorem.
.He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler's number.
.The Greek letter Σ for summations and the letter i to denote the imaginary unit
.Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function
.First to write f(x) to denote the function f applied to the argument x
A Swiss mathematician and physicist born in 1707
Introduced most modern day mathematical terminology and notation
He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory
.Euler was born on 15 April 1707
.He was the oldest of 3 siblings (2 sisters)
.At the age of thirteen he enrolled at the University of Basel, and in 1723, received his Master of Philosophy with a dissertation that compared the philosophies of Descartes and Newton