Table of Contents:
The Bridges of Konigsberg
The Value of Pi
Prime Numbers
Famous Paradoxes
The Problem of Points Proof of the Pythagorean Theorem

So what happened between 1220 and 1596? Well, in the late 15th century European mathematicians (benefiting from the greater intellectual freedom that came with the end of the Middle Ages) figured out how to express Pi exactly as an infinite product. This facilitated the computation of much better approximations. As time passed, mathematicians made the expressions for Pi as an infinite product or sum more concise, and computational methods improved as well. For example: François Viète (15401603) determined that:
John Wallis (16161703) showed that:
While Euler (17071783) derived his famous formula:
Today Pi is known to more than 10 billion decimal places.
to Finding the Value of Pi 
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