Which Pythagorean triples did the Sumerians know?

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Discussion Overview

The discussion revolves around the knowledge of Pythagorean triples by the Sumerians, specifically whether they were aware of certain triples such as (3, 4, 5) and (5, 12, 13). The scope includes historical analysis and references to ancient mathematical texts.

Discussion Character

  • Historical
  • Debate/contested

Main Points Raised

  • Some participants suggest that the Sumerians were aware of specific Pythagorean triples like (3, 4, 5) and (5, 12, 13).
  • One participant references a presentation that discusses clay tablets containing Pythagorean triplets, indicating that such knowledge existed.
  • Another participant cites the cuneiform tablet Plimpton 322, which contains 15 different Pythagorean triples, suggesting advanced mathematical understanding over 3,500 years ago.
  • There is a clarification that the term "Sumerians" is not interchangeable with "Babylonians," as the latter adapted the cuneiform developed by the former.
  • One participant notes that Plimpton 322 dates to around 1800 B.C., which is considered long after the Sumerian period.

Areas of Agreement / Disagreement

Participants express differing views on whether the Sumerians specifically knew about Pythagorean triples, with some supporting the idea based on historical texts and others emphasizing the distinction between Sumerians and Babylonians. The discussion remains unresolved regarding the extent of Sumerian knowledge.

Contextual Notes

There are limitations in the discussion regarding the definitions of Sumerians and Babylonians, as well as the historical timeline of mathematical developments. The references to specific tablets and their implications are not fully explored.

matqkks
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Where they aware of 3,4 and 5; 5, 12 and 13?
 
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From Wikipedia:

The cuneiform Plimpton 322 contains 15 different Pythagorean triples, e. g. ##(56,90,106)\, , \, (119,120,169)\, , \, (12709, 13500, 18541)##, which suggests that more than ##3,500## years ago a method of calculating such triples was already known.
 
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Btw., Wikipedia mentions Babylonians, not Sumerians. Those are not identical. The Sumerer developed the cuneiform, the Babylonians adapted it and followed the reign of the Sumerians.
 
fresh_42 said:
From Wikipedia:

The cuneiform Plimpton 322 contains 15 different Pythagorean triples, e. g. ##(56,90,106)\, , \, (119,120,169)\, , \, (12709, 13500, 18541)##, which suggests that more than ##3,500## years ago a method of calculating such triples was already known.
Thanks for this information. Very relevant to my question.
 
Plimpton 322 dates around 1800 B.C. long after the Sumerians.
 

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