-
Euler's Identity
The equation that links five of mathematics' most fundamental constants in a single line: e^(iπ) + 1 = 0.
-
Estimating π via polygons inscribed in a circle
Long before calculus, ancient mathematicians pinned down π by inscribing polygons with more and more sides inside a circle — one of them got seven decimal places right, by hand.
-
The Wallis Product
An infinite product with the numerator being the squares of the even integers and the denominator being the squares of the odd numbers having a surpising relation to π.
-
π is a Transcendental Number
Rational numbers, algebraic numbers, and then... transcendental numbers. It took 200 years after the term 'transcendental' first appeared in mathematics to prove that π was such a number.