ABSTRACT
Calculus and analysis represent some of the greatest developments in mathematics but are sometimes considered advanced and difficult. Yet even here there is room for very useful lateral thinking in the topics of infinite series, finding tangents, differentiation and integration, exponential functions, and weird objects such as a vessel which has infinite surface area but finite volume.
The wonderful arithmetic mean–geometric mean inequality shows up in this chapter too – for example, if a and b are positive real numbers, then (1/2)(a + b) is always greater than or equal to the square root of ab. This is one of the most spectacularly useful results in all of mathematics, with dozens of useful applications in many areas.
Calculus itself is a lateral notion from the minds of Newton and Leibniz and many other people, based on the idea that we can measure instant velocity and deal with infinitely small quantities precisely and accurately. It is one of the greatest achievements of humanity in any sphere and deserves to be more widely known and appreciated.
