Here are the homework problems from Chapter 1. 2. Use Egyptian techniques to divide 93 by 5. 8. A quantity, its 1/3, and its 1/4, added together, become 2. What is the quantity? (Problem 32 of the Rhind Papyrus) 9. Problem 72 of the Rhind Papyrus reads: 100 loaves of pesu 10 are exchanged for loaves of pesu 45. How many of these loaves are there? The solution given is, Find the excess of 45 over 10. It is 35. Divide this 35 by 10. _ _ You get 3 2. Multiply 3 2 by 100. Result 350. Add 100 to this 350. You get 450. Say then that the exchange is 100 loaves of pesu 10 for 450 loaves of pesu 45. Translate this solution into modern terminology. How does this solution demonstrate proportionality? ("pesu" is the inverse of the density of grain in the loaf: number of loaves divided by number of measures of grain.) 12. Show that 1 divided by 7 gives the sexagesimal fraction 0;8,34,17,8,34,17 ... by dividing in base 60. 14. In the Babylonian system, multiply 25 by 1,04 and 18 by 1,21. Divide 50 by 18 and 1,21 by 32 (using reciprocals) Use the standard modern multiplication algorithm modified for base 60. 18. Convert 1;24,51,10, the Babylonian approximation to the square root of 2, to decimals and determine the accuracy of the approximation. 24. Solve this problem from the Old Babylonian tablet BM13901: The sum of the areas of two squares is 1525. The side of the second square is 2/3 of that of the first plus 5. Find the sides of each square. 28. Solve the following problem from YBC4652: I found a stone, but did not weigh it; afer I subtracted one-seventh, added one-eleventh [of the difference], and then subtracted one thirteenth [of the previous total], it weighed 1 mina [= 60 gin]. What was the stone's weight?