Babylonian mathemathics (1)

Text
Mathematics is already well developed in the Old Babylonian period, by the 19th century BCE it had reached a full command of sexagesimal techniques based on a place value notation (though without a symbol for zero), including higher exponents and their inverses, and a great deal of insight into algebraic and plane geometric relations. Among them were “Thales’ Theorem” about the right triangle in a semicircle and also the “Pythagorean Theorem” for the right triangle. The famous Plimpton Tablet reveals full understanding of the mathematical laws which govern “Pythagorean” triples of integers, i.e., solutions of a² + b² = c² under the condition that a, b and c be integers. Here are only the first three solutions on which the text is based, going far beyond such trivialities as the discovery that 3² + 4² = 5²:
2,0 (= 120)² + 1,59 (= 119)² = 2,49 (=169)²
57,36 (= 3456)² + 56,7 (= 3367)² = 3,12,1 (= 11521)²
1,20,0 (= 4800)² + 1,16,41 (= 4601)² = 1,50,49 (= 6649)²

Since we have mathematical cuneiform texts from the Seleucid period and since Greek and Demotic papyri from the Graeco-Roman period in Egypt show knowledge of essentially the same basic material, one can not doubt that the discoveries of the Old Babylonian period had long since become common mathematical knowledge all over the ancient Near East. The whole tradition of mathematical works under the authorship of Heron (first century CE), Diophantus (date unknown), down to the beginning Islamic science (al-Khwarizmi, ninth century CE) is part of the same stream which has its ultimate sources in Babylonia.

Bibliography

Amar Annus

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