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Leonhard Euler

Mathematics

The Infinity of the Primes

21st September 2020 OldTrout 2521 Comments

Euclid’s Elements, Book IX, Proposition 20. Theorem : Prime numbers are more than any assigned multitude of prime numbers. That is, there are infinitely many primes. Proof : Suppose that there are primes : Let [more…]

Hobbies

From a Sum to a Product

20th January 2020 OldTrout 1947 Comments

In The Basel Problem we saw that Euler answered the question by showing that the sum of the reciprocals of the square numbers is equal to . That is The partial sums slowly converge to [more…]

OldTrout, Going Postal
Hobbies

A Beautiful Equation

18th November 2019 OldTrout 1972 Comments

Euler gave us this jewel which is regarded by many as the most beautiful equation in mathematics; it has both elegance and simplicity. It is comprised of five fundamental numbers and the operations of addition, [more…]

Hobbies

The Basel Problem

14th January 2019 OldTrout 5032 Comments

One sometimes gets very interesting results when one turns divergent sums upside down. The Basel problem was asked by Pietro Mengoli in . He asked what is the exact summation of the reciprocals of the [more…]

Hobbies

Euler’s Totient Function

6th August 2018 OldTrout 1964 Comments

Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all .  These numbers are called the totatives of . [more…]

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