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Writing and the wheel in Africa
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[QUOTE]Originally posted by Firewall: [QB] Here something about early african mathematics. [QUOTE] The Lebombo bone is the oldest known mathematical artifact. It dates from 35,000 BCE and consists of 29 distinct notches that were deliberately cut into a baboon's fibula. The Ishango bone is a bone tool, dated to the Upper Paleolithic era, about 18,000 to 20,000 BCE. It is a dark brown length of bone, the fibula of a baboon, with a sharp piece of quartz affixed to one end, perhaps for engraving or writing. It was first thought to be a tally stick, as it has a series of tally marks carved in three columns running the length of the tool, but some scientists have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting. These are the function postulated about the Ishango bones: 1. A tool for multiplication, division, and simple mathematical calculation; 2. A six-month lunar calendar;. a construct of a woman, keeping track of her menstrual cycle; In the book How Mathematics Happened: the First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10." see History of mathematics [/QUOTE]Nile Valley [QUOTE] The earliest attested examples of mathematical calculations date to the predynastic Naqada period, and show a fully developed numeral system. The importance of mathematics to an educated Egyptian is suggested by a New Kingdom fictional letter in which the writer proposes a scholarly competition between himself and another scribe regarding everyday calculation tasks such as accounting of land, labor and grain. Texts such as the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus show that the ancient Egyptians could perform the four basic mathematical operations—addition, subtraction, multiplication, and division—use fractions, compute the volumes of boxes and pyramids, and calculate the surface areas of rectangles, triangles, circles and even spheres[citation needed]. They understood basic concepts of algebra and geometry, and could solve simple sets of simultaneous equations. Mathematical notation was decimal, and based on hieroglyphic signs for each power of ten up to one million. Each of these could be written as many times as necessary to add up to the desired number; so to write the number eighty or eight hundred, the symbol for ten or one hundred was written eight times respectively. Because their methods of calculation could not handle most fractions with a numerator greater than one, ancient Egyptian fractions had to be written as the sum of several fractions. For example, the fraction two-fifths was resolved into the sum of one-third + one-fifteenth; this was facilitated by standard tables of values.[ Some common fractions, however, were written with a special glyph; the equivalent of the modern two-thirds is shown on the right. Ancient Egyptian mathematicians had a grasp of the principles underlying the Pythagorean theorem, knowing, for example, that a triangle had a right angle opposite the hypotenuse when its sides were in a 3–4–5 ratio. They were able to estimate the area of a circle by subtracting one-ninth from its diameter and squaring the result: Area ≈ [(8⁄9)D]2 = (256⁄81)r2 ≈ 3.16r2, a reasonable approximation of the formula πr2. The golden ratio seems to be reflected in many Egyptian constructions, including the pyramids, but its use may have been an unintended consequence of the ancient Egyptian practice of combining the use of knotted ropes with an intuitive sense of proportion and harmony. Based on engraved plans of Meroitic King Amanikhabali's pyramids, Nubians had a sophisticated understanding of mathematics and an appreciation of the harmonic ratio. The engraved plans is indicative of much to be revealed about Nubian mathematics. [/QUOTE]Sahelian [QUOTE] All of the mathematical learning of the Islamic world during the medieval period was available and advanced by Timbuktu scholars: arithmetic, algebra, geometry, and trigonometry. [/QUOTE]Other African traditions [QUOTE] One of the major achievements found in Africa was the advance knowledge of fractal geometry and mathematics. The knowledge of fractal geometry can be found in a wide aspect of African life from art, social design structures, architecture, to games, trade, and divination systems. With the discovery of fractal mathematics in widespread use in Africa, Ron Eglash had this to say, "We used to think of mathematics as a kind of ladder that you climb, and we would think of counting systems – one plus one equals two – as the first step and simple shapes as the second step. Recent mathematical developments like fractal geometry represented the top of the ladder in most Western thinking. But it's much more useful to think about the development of mathematics as a kind of branching structure and that what blossomed very late on European branches might have bloomed much earlier on the limbs of others. When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet." The binary numeral system was also widely known through africa before much of the world. It has been theorized that it could have influence western geomancy which would lead to the development of the digital computer. [/QUOTE]I found something about ancient trigonometry. History of trigonometry [QUOTE] Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They and later the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar method. The ancient Greeks transformed trigonometry into an ordered science. [/QUOTE] [QUOTE] Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemy expanded upon Hipparchus' Chords in a Circle in his Almagest. The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th century Indian mathematician and astronomer Aryabhata. These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry. At about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. Knowledge of trigonometric functions and methods reached Europe via Latin translations of the works of Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi. One of the earliest works on trigonometry by a European mathematician is De Triangulis by the 15th century German mathematician Regiomontanus. Trigonometry was still so little known in 16th-century Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. [/QUOTE]Note-in time this form of greek learning came to ancient nubia and sudan and some other areas in africa. In the middle ages of course islam and west africans advanced trigonometry and this info spread. In the other thread i should have said that meroe was known as a african athens and nubian alexandria. Alexandria is in africa. Ancient African Math/Science Shatters Stereotypes [QUOTE] Thousands of books and manuscripts uncovered in what is now Mali, especially around Timbuktu, are just being studied, with stunning results: African scholars in an unfathomably wealthy civilization independently developing sophisticated math, astronomy,and other sciences, even while Europe was still crawling out of the Middle Ages... From the world's oldest astronomical observatory to Timbuktu scholar Abul Abbas, who commented in 1723 on much earlier scholars' work in the same city - thus showing they were building an independent body of work (and whose conclusions show his lack of contact with, hence independence from, Europe),African mathematical and science achievements have heretofore been African mathematical and science achievements have here to fore been largely kept in the dark. All this, and so far only 14 out of more than 18,000 manuscripts have been translated and examined. [/QUOTE] [QUOTE] Timbuktu ... was one of the major cities of West Africa from 800 until just over400 years ago.It was very prosperous, and had many learning centers, with people collecting and writing books on law, poetry, astronomy,optics,mathematics. This history of scholarship in Africa extended over large parts of the continent. Ancient manuscripts are found all over West Africa and even in East Africa. They are written in Arabic and in local African languages. ...In Mali alone, there are around 200 private libraries, and literally hundreds of thousands of books. But most powerful in their refutation of the Eurocentric view of scientific development perhaps are the Mali manuscripts, some dating back 600 years, including beautifully drawn diagrams of the orbits of the planets in a geocentric universe, which demonstrate complex mathematical calculations and algorithms that were as accurate in some cases as anything we have today. And when as Muslims they needed to accurately determine the location of Timbuktu and Mecca, they surpassed the Greeks by inventing the functions of trigonometry. [/QUOTE] [/QB][/QUOTE]
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