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Answer:
Mathematics
Numbers, measurement and arithmetic
Around 3000 BC: Units of measurement are developed in the major Bronze Age civilisations: Egypt, Mesopotamia, Elam and the Indus Valley. The Indus Valley may have been the major innovator on this, as the first measurement devices (rulers, protractors, weighing scales) were invented in Lothal in Gujarat, India.[1][2][3][4]
1800 BC: Fractions were first studied by the Egyptians in their study of Egyptian fractions.
Geometry and trigonometry
2100 BC: The concept of area is first recognised in Babylonian clay tablets,[5] and 3-dimensional volume is discussed in an Egyptian papyrus. This begins the study of geometry.
Early 2nd millennium BC: Similar triangles and side-ratios are studied in Egypt (e.g. in the Rhind Mathematical Papyrus, a copy of an older Middle Kingdom text) for the construction of pyramids, paving the way for the field of trigonometry.[6]
Algebra
2100 BC: Quadratic equations, in the form of problems relating the areas and sides of rectangles, are solved by Babylonians.[5]
Number theory and discrete mathematics
2000 BC: Pythagorean triples are first discussed in Babylon and Egypt, and appear on later manuscripts such as the Berlin Papyrus 6619.[7]
Numerical mathematics and algorithms
2000 BC: Multiplication tables in Babylon.[8]
1800 BC – 1600 BC: A numerical approximation for the square root of two, accurate to 6 decimal places, is recorded on YBC 7289, a Babylonian clay tablet believed to belong to a student.[9]
19th to 17th century BCE: A Babylonian tablet uses 25⁄8 as an approximation for π, which has an error of 0.5%.[10][11][12]
Early 2nd millennium BCE: The Rhind Mathematical Papyrus (a copy of an older Middle Kingdom text) contains the first documented instance of inscribing a polygon (in this case, an octagon) into a circle to estimate the value of π.[13][14]
Notation and conventions
3000 BC: The first deciphered numeral system is that of the Egyptian numerals, a sign-value system (as opposed to a place-value system).[15]
2000 BC: Primitive positional notation for numerals is seen in the Babylonian cuneiform numerals.[16] However, the lack of clarity around the notion of zero made their system highly ambiguous (e.g. 13200 would be written the same as 132).[17]
Astronomy
Early 2nd millennium BC: The periodicity of planetary phenomenon is recognised by Babylonian astronomers.
Biology and anatomy
Early 2nd millennium BC: Ancient Egyptians study anatomy, as recorded in the Edwin Smith Papyrus. They identified the heart and its vessels, liver, spleen, kidneys, hypothalamus, uterus, and bladder, and correctly identified that blood vessels emanated from the heart (however, they also believed that tears, urine, and semen, but not saliva and sweat, originated in the heart, see Cardiocentric hypothesis).[18]
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