Noah ChetelatM. McLaughlinCalculus22 APR 14An Amateur's Brief History of CalculusIdeas preceding the concepts of functions, derivatives, and integrals were developed throughout the 17th century. What we call calculus “existed” as a set of ideas originating not only from Western Europe, but also from ancient Greece, the Middle East, India, China, and Japan . Abu Ali al-Hasan ibn al-Haytham, born in what is now southeastern Iraq, was renowned for his numerous books and his work in astronomy and optics. His interests were in geometry, algebra and number theory, and he was one of the first to integrate a fourth degree polynomial. Around 250 BC, Archimedes wrote a book – On Conoids and Spheroids – which demonstrated a method for determining the volume of the solid formed when a parabola rotates around its axis. At first glance, the verbal concept closely resembles the modern method of calculating this volume. However, after algebraic analysis, the two appear to have many differences. “In particular, if a and b are positive constants and we take the bounded region above b...