Homework Assignment 1

Homework Assignment 1 - product: (24,621.5) 2 (21,247.5) 2...

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Katie Medrek January 27, 2010 Math 161: Development of Mathematics Homework Assignment #1 1. Write the numbers 3,374 and 45,869 in the system used for transcribing cuneiform (in base 60). Answer : 3,374 = (3374 / 60) = 56, 14 And we can check this by: 56, 14 = 56 x 60 + 14 = 3,374 45,869 = (45,869 / 60) = 764, 29 = (764 / 60), 29 = 12, 44, 29 And we can check this by: 12, 44, 29 = 12 x 60 2 + 44 x 60 + 29 = 45,869 2. Multiply these two numbers following the "Babylonian" system (representing the product as the difference of the squares of the average and semi-difference). Write the product in sexagesimal notation. Answer : First, we find the average: (45,869 + 3,374) / 2 = 24,621.5 Then, we find the semi-defference: (45,869 - 3,374) / 2 = 21,247.5 Finally, we square the average and subtract it from the semi-difference squared, thus obtaining the
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Unformatted text preview: product: (24,621.5) 2 (21,247.5) 2 = product 606,218,262.3 451,456,256.3 = 154,762,006 The product should be written in sexagisimal notation: 154,762,006 = (154,762,006 / 60) = 2,579,366, 46 = (2,578,366 / 60), 46 = 42989, 26, 46 = (42,989 / 60), 26, 46 = 716, 29, 26, 46 = (716 / 60), 29, 26, 46 = 11, 56, 29, 26, 46 And we can check this by: 11, 56, 29, 26, 46 = (11 x 60 4 ) + (56 x 60 3 ) + (29 x 60 2 ) + (26 x 60) + 46 = 154,762,006 Also, check by: 12, 44, 29 x 56, 14 2, 58, 22, 46 11, 53, 31, 4 . 11, 56, 29, 26, 46 -- And we can see that this matches up with the average / semi-difference answer above, so this is the correct answer....
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This note was uploaded on 04/13/2010 for the course MATH 161 taught by Professor Cooke during the Spring '10 term at Vermont.

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