Using an infinite series, Isaac Newton calculated pi to 15 digits of precision.
Newton made this calculation in 1665 or 1666, during a remarkably productive period when he was developing ideas connected with calculus, infinite series, and analytical geometry. He used an arcsine series, transforming a trigonometric relationship into a form that could be evaluated term by term.
His result was extraordinary for the seventeenth century because infinite series allowed mathematicians to move beyond the limited precision of polygon-based geometric methods. Newton later joked about how far he had carried the calculation, writing that he was “ashamed” of the number of figures because he had little else to do at the time.
The result is sometimes confused with later records. James Gregory and Gottfried Wilhelm Leibniz developed important arctangent series, while John Machin calculated 100 digits in 1706. Newton's achievement was an early 15-digit approximation, not a modern record for pi.