Hobbies
From a Sum to a Product
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…]
Leonhard Euler
Hobbies
A Beautiful Equation
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
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
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…]