Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt () 3000 to c. , from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.
Written evidence of the use of mathematics dates back to at least 3200 BC with the ivory labels found in Tomb U-j at Abydos. These labels appear to have been used as tags for grave goods and some are inscribed with numbers. Further evidence of the use of the base 10 number system can be found on the Narmer Macehead which depicts offerings of 400,000 oxen, 1,422,000 goats and 120,000 prisoners. Archaeological evidence has suggested that the Ancient Egyptian counting system had origins in Sub-Saharan Africa. Also, fractal geometry designs which are widespread among Sub-Saharan African cultures are also found in Egyptian architecture and cosmological signs.
The evidence of the use of mathematics in the Old Kingdom (c. 2690–2180 BC) is scarce, but can be deduced from inscriptions on a wall near a mastaba in Meidum which gives guidelines for the slope of the mastaba. The lines in the diagram are spaced at a distance of one cubit and show the use of that unit of measurement.
The earliest true mathematical documents date to the 12th Dynasty (c. 1990–1800 BC). The Moscow Mathematical Papyrus, the Egyptian Mathematical Leather Roll, the Lahun Mathematical Papyri which are a part of the much larger collection of Kahun Papyri and the Berlin Papyrus 6619 all date to this period. The Rhind Mathematical Papyrus which dates to the Second Intermediate Period (c.
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Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Babylonian mathematics (also known as Assyro-Babylonian mathematics) are the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. With respect to time they fall in two distinct groups: one from the Old Babylonian period (1830–1531 BC), the other mainly Seleucid from the last three or four centuries BC.
An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction.
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