| [ history ] in KIDS 글 쓴 이(By): hobbes (& calvin) 날 짜 (Date): 1995년12월26일(화) 02시26분32초 KST 제 목(Title): [복사]guest(dofu):Babylonian mathematics The Babylonians had an advanced number system, in some ways more advanced than our present system. It was a positional system with base 60 rather than the base 10 of our present system. Now 10 has only two proper divisors, 2 and 5. However 60 has 10 proper divisors so many more numbers have a finite form. The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting has survived for 4000 years. To write 5h 25' 30", i.e. 5 hours, 25 minutes, 30 seconds is just to write the base 60 fraction, 5 25/60 30/3600 or as a base 10 fraction 5 4/10 2/100 5/1000 which we write as 5.425 in decimal notation. Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 BC. They give squares of the numbers up to 59 and cubes of the numbers up to 32. The table gives 8**2 = 14 which stands for 8**2 = 1 4 = 1*60 + 4 = 64 and so on up to 59**2 = 58 1 (58*60 + 1 =3481). One major disadvantage of the Babylonian system however was their lack of a 0. This meant that numbers did not have a unique representation but required the context to make clear whether 1 meant 1, 61, 3601, etc. One of the Babylonian tablets which is dated from between 1900 and 1600 BC contains answers to a problem containing Pythagorean triples, i.e. numbers a, b, c with a**2 + b**2 = c**2. It is said to be the oldest number theory document in existence. A translation of another Babylonian tablet which is preserved in the British museum goes as follows 4 is the length and 5 the diagonal. What is the breadth? Its size is not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? 3 times 3 is 9. 3 is the breadth. Clever, weren't they? |