Tag: continued fractions

Approximating Pi (Happy Pi Day)

Posted in Mathematics


Favorite Pi Approximations

What's your favorite \(\pi\) approximation?

Some of my favorite approximations of \(\pi\) come from Ramanujan-Sato series. These are mathematical series that generalize from a remarkable formula for \(\pi\) given by Srinivasa Ramanujan, an Indian mathematician:

$$ \pi^{-1} = \dfrac{\sqrt{8}}{99^2} \sum_{k \geq 0} \dfrac{ (4k)! }{ \left( 4^k k! \right …

Tags:    pi    continued fractions    number theory    mathematics    python    irrational numbers   

Computing Square Roots: Part 2: Using Continued Fractions

Posted in Mathematics


Table of Contents

Continued Fractions

Let's start part 2 of our discussion of computing square roots by talking about continued fractions. When we first learn mathematics, we learn to count in the base 10 system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can construct representations of all of the integers using these 10 digits, by arranging them in a different order. So, for example, saying 125 is equivalent to saying …