A famous formula for π:
π/4 = 1 − 1/3 + 1/5 − 1/7 + …
This comes from a trigonometry formula:
arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + …
Putting x = 1 gives the series for π/4.
This result was discovered independently by: Gottfried Wilhelm Leibniz (1673), James Gregory (1671), Nilakantha Somayaji (around 1500, in Tantrasangraha).