Euclid’s omission was a signal that something deeper was needed. To come to grips with π’s numerical value required a new kind of mathematics, one that could cope with curved shapes. How to measure the length of a curved line or the area of a curved surface or the volume of a curved solid — these were the cutting-edge questions that consumed Archimedes and led him to take the first steps toward what we now call integral calculus. Pi was its first triumph.
