The Volume of a Donut? 3D Geometry and Integral Calculus Proofs скачать в хорошем качестве

The Volume of a Donut? 3D Geometry and Integral Calculus Proofs

How can we determine the Volume of a Donut? It can be derived through multiple interesting and unique approaches, namely, in a geometric and calculus proof. 0:00 Introduction 0:26 Archimedes' Method 1:12 Application to Torus 3:03 Describing a Function 3:39 Integral Calculus 6:45 Conclusion P.S. At 4:45 I make a trigonometric substitution for the integral even though it can be recognised that it describes the area of a semicircle. This makes the problem longer and appear more complex than it may be. However, it does make the proof feel more complete. You also don't get the chance to solve an integral like this every day, it was an aesthetic choice. 20/04/24