Basel problem

The set of square numbers is small (see Basel problem).

(the demonstration of this equality is known as the Basel problem)

The reciprocals of square numbers produce a convergent series (the Basel problem):

His daring (and, by modern standards, technically incorrect) use of power series enabled him to solve the famous Basel problem in 1735:

Another application of this Fourier series is to solve the Basel problem by using Parseval's theorem.

The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct.

The Basel problem is posed by Pietro Mengoli, and will puzzle mathematicians until solved by Leonhard Euler in 1731.

The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:

Leonhard Euler solves the Basel problem, first posed by Pietro Mengoli in 1644, and the Seven Bridges of Königsberg problem.

The Basel problem is a famous problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735.

Euler had already become famous for finding the values of these functions at positive even integers (including the Basel problem), and he was attempting to find the values at the positive odd integers (including Apéry's constant) as well, a problem that remains elusive today.

She later warms up to Tetra, though, when she sees that she is earnestly pursuing mathematical studies with the narrator, and after she hears that Tetra has independently come up with an idea that leads to an elegant solution to the Basel problem, they become close friends.