3-Mathematics-History-Ancient Mathematics

Mesopotamian calendar

It had 12 months and predicted yearly flooding.

Egyptian calendar

Year was 365 days long, with 12 months of 30 days. Calendar predicted Nile flooding.

Sun and Moon position

Babylonian mathematicians predicted Sun and Moon positions.

Ahmes

He lived -1680 to -1620, solved practical architecture problems, calculated astronomical events, and used simple interest, compound interest, principal, and rate. Multiplication is repeated doubling, and division is repeated halving.

Pythagoras math

He lived -580 or -569 to -500 and invented gnomon and Pythagorean theorem. He used similar figures, proportions, Pythagorean triples, Golden Ratio, Golden Section, and Golden Rectangle, and triangular, square, perfect, amicable, and prime numbers.

sexagesimal number system

Babylonian mathematicians used number system based on 60 {sexagesimal number system}. They predicted Sun, Moon, and planet positions based on previous positions that they had recorded.

Platonists old

Platonists used inference, proof, deduction, and induction. They studied regular polyhedra, conic sections, prism, pyramid, cone, cylinder, perimeter, area, volume, and surfaces. Regular polyhedra are tetrahedron, icosahedron, and dodecahedron.

Platonists middle

Platonists studied prisms, pyramids, cylinders, cones, conic sections, and the five regular polyhedra. They gave circle 360 degrees. They assumed proposition is true and then deduced consequences, until statement is clearly true or false {method of analysis}. They assumed theorem and showed that theorem leads to contradiction, so theorem is false {reductio ad absurdum, Platonists}. They used deductive proof {deduction, Platonists}.

Surya Siddhanta

It depends on Persian books.

Tabit ibn Qorra

He lived 836 to 901.

al-Battani

He lived 868 to 929 and found ecliptic angle and solar-year length.

al-Hazen

He lived 965 to 1039 and studied perspective, projection, vanishing points, and cubic equations.

Bhaskara

He lived 1114 to 1185, followed Brahmagupta, and used combinations and permutations.

al-Kashi J

He lived 1390 to 1450 and used base-ten number system, decimals, and negative powers.

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Date Modified: 2022.0225