Take it to the limit one more time – a history of calculus I

The concept of infinity lies at the heart of calculus, the infinitely large and the infinitely small, also known as the infinitesimal. In fact, in the early days of calculus, at the beginning of the eighteenth century, it was known as infinitesimal calculus. Springing forward to my schooldays, integral calculus was introduced by looking at the area under a curve produced by a function drawn in a Cartesian coordinate system. This area between two given values on the x-coordinate, in divided in to equal rectangles. The area of under the curve between those coordinates is equal to the sum of the areas of the rectangles plus the areas of the little triangles left between the top of the rectangles and the curve, which are not easy to calculate. By making the rectangles stepwise narrower those triangles become smaller and smaller until the rectangles are infinitesimally wide, when the triangles cease to exist and the area under the curve becomes the sum of the areas of the rectangles. Of…