# Talk:Babylonian mathematics

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## Babylonian multiplication formulae

How do we know that the Babylonians used

$ab = \frac{(a + b)^2 - a^2 - b^2}{2}$
$ab = \frac{(a + b)^2 - (a - b)^2}{4}$

rather than

$ab = \frac{a^2 + b^2 - (a-b)^2}{2}$?

If one is calculating from a table of squares of the numbers from 1 to $N,$ the last formula works for the product of any $a$ and $b$ that are both in the table, i.e. in the range $1..N.$ The two earlier formulae require that the sum, $a + b$, also be in the range $1..N.$ What evidence do we have that the Babylonians used the first two formulae, but not the third? Alma Teao Wilson (talk) 21:26, 16 October 2008 (UTC)

## Critique on the use of algebra for explanations

Using algebra to explain how babylonians did math suggests they set up equalities and derived new equations from old using an algebraic system This seems unlikely; the likely truth is that they assembled formula that were useful for solving particular problems either by insight or experiment. You need to include actual text or literal translations of their method.Mrdthree 23:58, 6 April 2006 (UTC)

I've removed some text some of which seems to have been copied from [1], as a potential copyright violation. Paul August 15:21, 21 June 2006 (UTC)

I've restored the text on the Chaldeans, most of which came from the Hipparchus article (although I'm not sure about the original sources). The Old Babylonian section however would need to be re-written without directly copying from the History of Mathematics archive. Jagged 18:16, 21 June 2006 (UTC)
I have trimmed, re-written, wikified and re-ordered the Old Babylonian Mathematics section. I think it is now sufficiently different from the source to be no longer copyvio, so I have put the re-written version back into the article. Gandalf61 13:20, 22 June 2006 (UTC)
Well done. Paul August 20:19, 22 June 2006 (UTC)

## Name of the article

The current name (Assyro-Babylonian mathematics) was changed to without discussion, let ous establish the articles name based on WP:NAME.

• hits:7 ; books: 32; scholar: 2
• hits:12,500 ;books: 742; scholar: 642

Clearly the most recognizable name is Babylonian mathematics and not Assyro-Babylonian matematics. So what's the reason for the name change on the article? The TriZ (talk) 02:51, 26 November 2008 (UTC)

I'll change back the article to its original name. Feel free to reach consensus next time you move a page. The TriZ (talk) 03:03, 28 November 2008 (UTC)

## Shoddy wording

In the opening paragraph: "...accurate to nearly six decimal places." Does this mean it was 'accurate to five decimal places'?--FimusTauri (talk) 12:37, 28 January 2009 (UTC)

Fixed it myself.--FimusTauri (talk) 11:30, 5 March 2009 (UTC)

## Divisors

In the text, the divisors of 60 are given, but with 1 and 60 left out. —Preceding unsigned comment added by 86.137.170.8 (talk) 12:26, 28 July 2009 (UTC) 1 and 60 have now been added to the list. —Preceding unsigned comment added by 86.184.201.103 (talk) 09:16, 19 April 2010 (UTC)

## Pioneers

The Babylonians are said to be pioneers in using the base 60. The article on Babylonian numerals correctly points out that it was inherited from the Sumerians. —Preceding unsigned comment added by 78.105.36.65 (talk) 14:45, 10 October 2009 (UTC)

## Angles

The article starts out by crediting Babylonian use of base 60 with such things as dividing a circle into 360 degrees, and then later states that ancient Babylonian mathematicians had no concept of the measures of angles, but only used computations related to the sides of triangles, which seems to be a contradiction. Did they use triangle measure in their astronomy too? Or was it simply that they found computations based upon triangle sides easier for terrestrial use? — Preceding unsigned comment added by 166.70.15.233 (talk) 14:37, 14 August 2011 (UTC)

## Plimpton

"Though the table was formerly popularly interpreted by leading mathematicians as a listing of Pythagorean triples and trigonometric functions, in 2002 the Mathematical Association of America published Robson's research and (in 2003) awarded her with the Lester R. Ford Award for a modern day interpretation formally rejecting prior mathematical misconceptions."

This goes too far in several ways.

• Publishing historical research does not mean enshrining it as the ultimate truth. (The same goes for scientific research, for that matter, but in the case of history, this has to be emphasised particularly strongly.)
• For that matter, MAA is mostly an association of mathematics educators, not the main association of professional mathematicians (AMS). (This is of course by no means the main issue.)
• Two issues are mixed here. It may be more or less clear by now that interpreting Plimpton 322 as a trigonometric table may be an anachronism. At the same time, Plimpton 322 is a table of Pythagorean triples (in the sense of valid integer or rational lengths of a triangle), and the language of the headings suggests that it was also conceived as such.
• Robson's papers on the subject are written in a polemical style (as she herself says in one of them). This is common practice in parts of history (perhaps especially ancient history?) -- in order to make some headway, you have to be polemical. It is (a) not common practice among mathematicians writing about their subject, (b) not something that, by itself, makes her work a definitive rebuttal of previous work.

The following paragraph in her work is key:

[...] the question “how was the tablet calculated?” does not have to have the same answer as the question “what problems does the tablet set?” The first can be answered most satisfactorily by reciprocal pairs, as first suggested half a century ago, and the second by some sort of right-triangle problems.

(E. Robson, "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322", Historia Math. 28 (3), p. 202). We would be much better off by putting this forward (as a view with strong support) than by being led off by an arguably inaccurate and overly enthusiastic interpretation of the polemics that precede it. Garald (talk) 08:57, 6 October 2011 (UTC)

Regarding the statement "The triples are too many and too large to have been obtained by brute force." I am no polished mathematician, but in my youth managed to develop a crude algorithm for generating Pythagorean triplets (PTs) in a few hours simply by pondering and playing with a hand written table of squares. This was pre-internet, with no reference to other mathematicians or mathematical works. So it shouldn't seem incredible that the Plimpton 322 tablet had either "too many" or "too large" examples. The size of algorithm-generated PTs are arbitrarily chosen by the size of the starting values used. See "Pythagorean Triplets" here on Wikipedia for more detail. — Preceding unsigned comment added by Sarookha (talkcontribs) 15:26, 26 November 2012 (UTC)