Story of Maths - Part 1.1: Egyptian mathematics "Story of maths" is a BBC TV show presented by Marcus du Sautoy, a mathematician (specialized mainly in group theory and number numb theory) and professor at the University of Oxford.
1. The language of the universe A. Egyptian mathematics It's around the river Nile that some of the first signs of mathematics as we know it today emerged. Around 6000 BC, people abandoned nomadic life and began to settle there. Ancient Egyptians needed to calculate the date of the flooding of the Nile, the area of their land, the amount of taxes charged and collated... People needed to count and measure. There was a very strong link between bureaucracy and the development of mathematics in ancient Egypt: It was vital to know the the area of a farmer's land so he could be taxed accordingly. The Egyptians invented some of the first numbers in history: the units of measurement were inspired by body parts: a palm was the width of a hand, and a cubit an arm length from elbow to fingertips. fingertips. They were using a decimal system, motivated by the 10 fingers on our hands. The sign for one was a stroke, 10, a heel bone, 100, a coil of rope, and 1,000, a Lotus plant. The hieroglyphs are beautiful, but the Egyptian number system was fundamentally flawed. flawed. They had no concept of a place value: if you want to write a million minus one, then the poor old Egyptian scribe has got to write nine strokes, nine heel bones, nine coils of rope, and so on, a total of 54 characters. Despite the drawback of this number system, the Egyptians were brilliant problem solvers. The Rhind Mathematical Papyrus was recorded by a scribe called Ahmes around 1650BC. It explicitly states how multiplications and divisions were carried out, and explains the use of fractions; the point oint of this papyrus is to find solutions to everyday situations. One of the earliest representations of fractions came from a hieroglyph which had great mystical significance: it's called the th Eye of Horus. Horus was an Old Kingdom god, depicted as half man, half falcon. According to legend, Horus' father was killed by his other son, Seth. Horus was determined to avenge the murder. During one particularly fierce battle, Seth ripped out Horus' eye, tore it up and scattered it over Egypt. But the gods were looking favorably on Horus. They gathered up the scattered pieces and reassembled the eye. Each part of the eye represented a different fraction. This is the first hint of something called a geometric series, and it appears at a number of points in the Rhind Papyrus. In the Rhind Papyrus, we also find the area of the circle. What is astounding in the exactness of this area's calculation; but the texts we have do not show us the methods that were used to find it. And because the area of a circle is Pi times the radius squared, the Egyptian calculation gives us the first accurate value for Pi. But there's another imposing and majestic symbol of Egyptian mathematics : the pyramid. Some have suggested the golden ratio might be hidden inside the proportions of the Great Pyramid. But the most impressive thing about the pyramids is the mathematical brilliance that went into making them, including the first inkling of one of the great theorems of the ancient world, Pythagoras' theorem. In order to get perfect right-angled right angled corners on their buildings and pyramids, the Egyptians would have used a rope with knots tied in it: at some point, the Egyptians realized that if they took a triangle with sides marked with three knots, k four knots and five knots, it guaranteed them a perfect right-angle. angle. But the Egyptians worked with concrete, given numbers, and there's no general proof within the Egyptian mathematical texts. It would be some 2,000 years before the Greeks and Pythagoras would prove that all right-angled right angled triangles shared s certain properties. This wasn't the only mathematical idea that the Egyptians would anticipate. In a 4,000-year-old 4,000 old document called the Moscow papyrus, we find a formula for the volume of a pyramid with its peak sliced off, which shows the first hint of calculus at work.
