Calculus from Many Springs — How Change and Accumulation Became One Language
Begin with area in Syracuse, a circle in Luoyang, measurement in Baghdad and Cairo, instantaneous motion at Ujjain, and series at Sangamagrama. Then cross the shoulders built by Kepler, Cavalieri, Fermat, Descartes, and Barrow before Newton and Leibniz bind change and accumulation in different languages. Bernoulli, Euler, Agnesi, Lagrange, Fourier, Cauchy, Weierstrass, and Maxwell carry that language into textbooks, mechanics, heat, rigor, and fields across twenty-four scenes.
Scene 1 of 24
c. 250 BCE
Syracuse
Filling without End while Keeping Hold of the Answer — Archimedes' Parabola
Archimedes inscribed a triangle in a parabolic segment, filled the gaps with smaller triangles, and proved geometrically that their continuing sum was four-thirds of the first. Infinite summation and upper and lower bounds meet here, but coordinate functions, a modern definition of limit, and Riemann integration should not be projected backward onto the argument.
Replay on the map from scene 1Scene index