## Simple proofs: Archimedes’ calculation of pi

MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\$$‘,’\$$’]]}});

Credit: Ancient Origins

Introduction

Archimedes is widely regarded as the greatest mathematician of antiquity. He was a pioneer of applied mathematics, for instance with his discovery of the principle of buoyancy, and a master of engineering designs, for instance with his “screw” to raise water from one level to another. But his most far-reaching discovery was the “method of exhaustion,” which he used to deduce the area of a circle, the surface area and volume of a sphere and the area under a parabola. Indeed, with this method Archimedes anticipated, by nearly

Continue reading Simple proofs: Archimedes’ calculation of pi

## Simple proofs: The fundamental theorem of calculus

MathJax TeX Test PageMathJax.Hub.Config({tex2jax: {inlineMath: [[‘$’,’$’], [‘\$$‘,’\$$’]]}});

Isaac Newton, Credit: sjisblog.com

Introduction: The fundamental theorem of calculus, namely the fact that integration is the inverse of differentiation, is indisputably one of the most important results of all mathematics, with applications across the whole of modern science and engineering. It is not an exaggeration to say that our entire modern world hinges on the fundamental theorem of calculus. It has applications in astronomy, astrophysics, quantum theory, relativity, geology, biology, economics, just to name a few fields of science, as well as countless applications in all types of engineering — civil,

Continue reading Simple proofs: The fundamental theorem of calculus