Mathematics in Babylon

choi

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Edward Rothstein, Masters of Math, From Old Babylon; A precursor to the
theoretical flowering of Greek math. New York Times, Nov. 27, 2010.
http://www.nytimes.com/2010/11/27/arts/design/27tablets.html?_r=1&scp=3&sq=cuneiform&st=cse

Note:
(a) Pythagoras (c. 570- c. 495 BC)
Wikipedia
(b) The report states, "But Neugebauer, and then his many students and rivals, also showed how sophisticated Babylonian mathematics was and how many similarities existed to later Western systems ?if, that is, you counted using 60 fingers (as we often seem to, thanks to the Babylonians, when dealing with seconds and minutes and, in part, even when measuring angles)."

The last clause refers to sexagesimal.

(i) sexagesimal (adj or n; Latin sexagesimus sixtieth, from sexaginta sixty): "of, relating to, or based on the number 60"

All English definitions are from
http://www.merriam-webster.com

(ii) Babylonian numerals
http://en.wikipedia.org/wiki/Babylonian_numerals

Quote:

"The Babylonians, who were famous for their astronomical observations and calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from the Sumerian and also Akkadian civilizations. Neither of the predecessors was a positional system

"The legacy of sexagesimal still survives to this day, in the form of degrees (360?in a circle or 60?in an angle of an equilateral triangle), minutes, and seconds in trigonometry and the measurement of time, although both of these systems are actually mixed radix.

* radix (n; Latin for "root"): "the base of a number system or of logarithms"

My comment: The "base" here means 10 (we use) and 60 (Babylonians used).

** mixed radix
http://en.wikipedia.org/wiki/Mixed_radix

In this eexample: a week has the base of 7; hour, 24; both minute and second, 60.
  

(c) The report mentions "the bird抯 feet of Babylonian numerals."

It means that Babylonian numerals look like bird's feet. See the previous link.

(d) The report says, "The same digit for us has a different value if it is in the 1抯 column, the 10抯 column, or the 100抯 column; the Babylonians could use the same sign, depending on context, to represent a 1 or a 60 or a 3,600."
  
See
positional notation
http://en.wikipedia.org/wiki/Positional_notation

(e) Plimpton 322
http://en.wikipedia.org/wiki/Plimpton_322
(Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University)

(f) ephemera (n; New Latin, from Greek ephēmera, neuter plural of ephē
meros; plural ephemera also ephemerae or ephemeras): " something of no
lasting significance 梪sually used in plural"
http://www.merriam-webster.com/dictionary/ephemera?show=0&t=1290881827  

(g) A Culture of Mathematics: slide show (online only).
http://www.nytimes.com/slideshow/2010/11/18/science/20101123-babylon.html?scp=4&sq=cuneiform&st=cse


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