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- Euler proved that the fifth Fermat number 210 + 1 isn't prime.
- He proved that all even perfect numbers can be expressed as N = 2p-1(2p-1), where p is some Prime number.
- He found 60 amicable numbers at a time when only 3 were known.
- He was the first person to use the symbol e to represent the irrational number 2.7128...
- He proved that e is irrational.
- He popularized the symbol À for the irrational number 3.1415...
- He introduced the symbol Σ to represent summation.
- He showed that powers could be imaginary or complex numbers.
- He developed the trigonometric expansion of À/2.
- He invented graph theory.
- He developed the Euler's constant, which is an approximation of the sum of the harmonic series.
- He proved Fermat's last theorem for n = 4; i.e that x4 + y4 = z4 can't be solved with positive integers for x, y, and z.
- He developed the notation f(x) for functions.
- He found the geometric result known as Euler's characteristic, V + F - E where V is the number of vertices, F is the number of faces, and E is the number of edges of a polyhedra that is topologically equivalent to a sphere, which directly lead to the invention of the mathematical discipline known as topology.
- He developed Euler's formula, eix = cos(x) + isin(x), where i is the imaginary number.
- He invented the mathematical discipline known as the calculus of variations.
- He introduced the zeta function as an infinite series, ζ(s) = Σ∞n=1(1/ns), and related it to an infinite product over all of the prime numbers pn, ζ(s) = Π∞n=1(1-1/pns)-1.
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What did Leonhard Euler do for math?
Leonhard Euler made many contributions to math but the one thing he is most famous for is changing the base of the natural logarithim by using the letter e which is aka Euler's number
Who introduced the math symbol e?
Leonhard Paul Euler
Who came up with the little e in math?
Leonhard Euler, a aswiss mathematician, started to use the letter e for the constant in 1727. The first book mentioning it is Euler's Mechanica (1736)
What is the difference between an Euler circuit and an Euler path?
The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.
Who calculated the value of e?
Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).
