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By L. Auslander, R. Tolimieri

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By L. Auslander, R. Tolimieri

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Tex 24 11/03/2009 18:11 Con rming Pages 25 Number Recording of the Babylonians and confusion could result. Someone recopying the tablet might not notice the empty space, and would put the gures closer together, thereby altering the value of the number. C. on, a separate symbol or called a divider, was introduced to serve as a placeholder, thus indicating an empty space between two digits inside a number. With this, the number 84 was readily distinguishable from 3624, the latter being represented by The confusion was not ended, since the Babylonian divider was used only medially and there still existed no symbol to indicate the absence of a digit at the end of a number.

That is, he multiplied the selected expression by the odd integer n to produce 2. Nowhere is there any inkling of the technique used to arrive at the decomposition. Fractions 2=n whose denominators are divisible by 3 all follow the general rule 2 1 1 D C : 3k 2k 6k Typical of these entries is 2 15 (the case k D 5), which is given as 2 15 D 1 10 C 1 : 30 If we ignore the representations for fractions of the form 2=(3k), then the remainder of the 2=n table reads as shown herewith. 2 5 2 7 2 11 2 13 2 17 2 19 2 23 2 25 2 29 2 31 2 35 2 37 2 41 2 43 2 47 2 49 2 51 D D D D D D D D D D D D D D D D D 1 1 C 15 3 1 1 C 28 4 1 1 C 66 6 1 1 1 C 52 C 104 8 1 1 1 C 51 C 68 12 1 1 1 C 76 C 114 12 1 1 C 276 12 1 1 C 75 15 1 1 1 C 58 C 174 C 24 1 1 1 C 124 C 155 20 1 1 C 42 30 1 1 1 C 111 C 296 24 1 1 1 C 246 C 328 24 1 1 1 C 86 C 129 C 42 1 1 1 C 141 C 470 30 1 1 C 196 28 1 1 C 102 34 1 232 1 301 2 53 2 55 2 59 2 61 2 65 2 67 2 71 2 73 2 77 2 79 2 83 2 85 2 89 2 91 2 95 2 97 2 101 D D D D D D D D D D D D D D D D D 1 1 1 C 318 C 795 30 1 1 C 330 30 1 1 1 C 236 C 531 36 1 1 1 1 C 244 C 488 C 610 40 1 1 C 195 39 1 1 1 C 335 C 536 40 1 1 1 C 568 C 710 40 1 1 1 1 C 219 C 292 C 365 60 1 1 C 308 44 1 1 1 1 C 237 C 316 C 790 60 1 1 1 1 C 332 C 415 C 498 60 1 1 C 255 51 1 1 1 1 C 356 C 534 C 890 60 1 1 C 130 70 1 1 1 C 380 C 570 60 1 1 1 C 679 C 776 56 1 1 1 1 C 202 C 303 C 606 101 Ever since the rst translation of the papyrus appeared, mathematicians have tried to explain what the scribe’s method may have been in preparing this table.

Describe a simple rule for multiplying any Egyptian number by 10. 1000 5000 10,000 50,000 Other numbers were made up on an additive basis, with higher units coming before lower. Thus each symbol was repeated not more than four times. An example in this numeration system is 5. Write the Ionian Greek numerals corresponding to (a) 396. (b) 1492. (c) 1999. (d) 24,789. (e) 123,456. (f) 1,234,567. 6. Convert each of these from Ionian Greek numerals to our system. (a) (b) 0 Þ¦ ½Ž. 0 þÞ. " (c) M 0" ¹".

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