Plimpton 322 : A Universal Cuneiform Table for Old Babylonian Mathematicians, Builders, Surveyors and Teachers

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Abstract

This article deals with the damaged and incomplete Old Babylonian tablet Plimpton 322 which contains 4 columns and 15 rows of a cuneiform mathematical text. It has been shown that the presumed original table with its 7 columns and 39 rows represented: a table of square roots of numbers from 0 to 2 for mathematicians; an earliest rudiments of a trigonometric table for builders and surveyors where angles are not measured as an arc in a unit circle but as a side of a unit right-angled triangle; a list of the 39 exercises on reciprocal pairs, unit and integer-side right triangles (rectangles), factorization and square numbers for teachers.

The article provides new arguments in favor of old disputes (squares of diagonals or widths; mistakes in previous analysis of errors in P322). Contradictory ideas about P322 are discussed: Is it the table of triangle sides or factorization terms? Was it compiled by a parallel or independent factorization of the sides or of their squares? Are sides of an initial unit triangle enlarged or reduced by such a factorization? Does it contain two or four arithmetical errors?

Time and dimensional requirements for calculation and writing of the complete tablet have been also estimated.

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Tatra Mountains Mathematical Publications

The Journal of Slovak Academy of Sciences

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CiteScore 2017: 0.37

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researchers in the all fields of mathematical research

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