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Babylonian Maths

25 August 2017
Ancient history

William sent this one in. It is also in various other places such as https://tallbloke.wordpress.com/2017/08/24/mathematical-mystery-of-ancie… … and https://wattsupwiththat.com/2017/08/25/3700-year-old-babylonian-tablet-r… … where we learn a clay tablet that has lain undecyphered for many years has now been solved by a team from New South Wales University in Australia. It dates back to somewhere between 1822 and 1762BC and it appears it is based on Pythagoran triples and uses a kind of trigonometry based on ratios, rather than angles and circles. It seems it is actually a trigonometry table, presumably used by architects to construct temples, palaces, and major building enterprises. However, unlike modern trigonometry Babylonian mathematics used a base of 60 (a sexagesimal system) rather than 10 as we do nowadays. 60 is easier to divide by 3 and calculations appear to be more accurate than the modern system (it is claimed).

In the comments it is posited we still use 60 oriented mathematics in things such as time and navigation (60 minutes and 360 degrees). Contrary to the tone of the press release the 60/360 measurement system in the ancient world has been fairly well documented and that Pythagoras may have got some of his ideas from Babylonia is a well known fact. This knowledge was probably used by the researchers to decypher the tablet. Without that knowledge it may still be a jumble of numbers. 

Another commenter points out that without a measuring tool in the hand one can still revert to ratios – and carpenters, among others, use them on a regular basis (which may refer to a minority of carpenters). The invention of a table of ratios is the next logical step up from ratios and would have been especially useful to people engaged in a large building project. Mechanisation has seduced humans into thinking they are smarter than the ancients – but this tablet shows they are not.

See also https://melitamegalithic.wordpress.com/2017/04/17/melita-megalithic/ … where he suggests that four or five thousand years ago the Earth's orbit was nearer a circular one, rather than elliptical, hence a year of 360 days (if I understood him right). Of course, that is not to say he is right but it is perhaps another way to get a 360 day year rather than a change in the axis of rotation. Most of us have played around with a compass as a child , drawing patterns such as six petalled flowers within a circle etc. However, the author says a circular orbit would have been important for ancient people to figure out earth's motion relative to the Sun (even if the orbit was not circular0. The 360 day year is arithmetical convenience he suggests – although the number of days in the year could have been changing as a result of polar ice loading (as an example). The changing moment of inertia may have affected rotational time – as in day length (more or less days per orbit).

See also http://nrich.maths.org/6070 … and www.dioi.org/                                                                                                     

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