How to Integrate with an AX? The Surprising Power of Planimeters – Visually Explained!

描述

Today’s mission is to reveal a surprisingly simple trick that lets you use any old ax(e) to calculate the area of plane shapes. More broadly, we’ll explore planimeters — mechanical instruments that compute area by tracing a shape’s edge. Real mathematical magic in action! 00:00 Intro (a mathematical fairy tale) 07:16 Cool machines (history and types of planimeters) 09:05 Green's theorem (the most common high-level calculus explanation) 13:05 Easy peasy (the easiest and at the same time pretty rigorous explanation) 20:30 Full sweep (the best but somewhat handwaivy explanation) 26:50 AX (making