History of Calculus: Part 2 - Calculus in the Ancient World

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This is part 2 of the series: History of Calculus. Where I talk about the origins of calculus from ancient times to modern history. In this video I talk about the first two of the five methods that calculus evolved from: The method of dissection in ancient Egypt and the method of exhaustion in ancient Greece. I believe that the best way to understand a complex topic is to go through its history and see how it evolved over the years step by step. My aim is to make calculus, and other more complex topics, accessible and enjoyable and to tell their fascinating stories that sometimes spanned thousands of years. Support this channel Your support of the channel is very much appreciated. You can do so at the links below. Thanks for keeping me going :) - Buy me a coffee: https://www.buymeacoffee.com/tareksaid - Support me on PayPal: http://bit.ly/3FLja7L - Patreon: patreon.com/tareksaid Notes - 00:30 The rope stretchers had a great reputation in the ancient world. For example, when the Greek geometer Democritus (460 B.C - 370 B.C) wanted to boast about his geometric abilities, he claimed that not even the "rope stretchers" excelled him. - 1:05 According to Ahmes, the scribe who wrote the papyrus that was later named after him, the material in the papyrus was derived from a much older prototype that dates back to the middle kingdom (2000 B.C - 1800 B.C) and it is possible that some of the knowledge was handed down from Imhotep, the Architect to the Pharaoh Zoser, who supervised the building of the oldest pyramid in Egypt (the step pyramid) (A History of Mathematics | Carl B. Boyer) - The papyrus was bought in 1858 in a Nile resort town by Henry Rhind, hence the modern name. It is currently in the British Museum. It has the following Museum Number: EA10058 - 1:36 The dissection method mentioned here is an elementary form of the more advanced method of the 19th century. - 2:14 The khet equals 100 cubits (another Ancient Egyptian unit). 1 khet = 45.72 meters - 3:00 The translation of the triangle problem (problem 51) in Ahmes Papyrus is: "Example of calculating a triangle of land. If it is said to you: A triangle of 10 khet in its height and 4 khet in its base. What is its acreage? The doing as it occurs : You are to take half of 4, namely 2, in order to give its rectangle. You are to multiply 10 by 2. This is its acreage." (The Rhind Mathematical Papyrus | T. Eric Peet) - 4:38 The Greeks also considered the straight line as a curve and placed it with the circle in the first rank. - 6:17 No known bust of Antiphon exists. This is a bust of an unknown man from Ancient Greece. - 6:50 At the time of Antiphon, infinity wasn't properly understood. Hence the reason it is not clear whether he meant an infinite-sided polygon, or just a many-sided polygon, would equal to a circle. - 8:55 It is not known who was the first person to come up with the formula of the circle: 1/2 r c. Probably because it was based on shaky logic and the Greeks cared more about the method than the result. It was certainly known before Archimedes, but he did prove this formula, hence the reason it is attributed it to him. - 10:50 Archimedes infinitesimal method is known as "the method". It was discovered, miraculously, in a 13th century prayer book. The text of the method was scraped off (a common practice at the time in order to reuse the animal skin parchment which was expensive) and prayer text was written over it. Luckily, the scraping was not done properly and the faint mathematical text was still legible. For more information look up: Archimedes Palimpsest. References: - Proposed Origin of Geometry: An Account of Egypt - Herodotus | Translated by G. C. Macaulay - Ahmes (Rhind) Papyrus: The Rhind Mathematical Papyrus | T. Eric Peet - The number and ranking of curves in Ancient Greece: Historical Stages in the Definition of Curves | Carl B. Boyer - Method of Exhaustion: A History of Greek Mathematics | Sir Thomas Heath - Archimedes' Infinitesimal Method : The Method of Archimedes | Sir Thomas Heath