Homework 5

Reminder: You can (and are encouraged to) discuss problems with your classmates. Then write down the answers by yourself.

1. (Only Lecture 1. Lecture 2 does not have Problem 1 since we did not cover magic squares.) Recall that Magic Squares were constructed in Ancient China. Can you construct a magic square of size 3x3 with a number different from 5 in the center? Justify your answer
2. Write a short paragraph describing why each of the following societies believe in a mathematical statement, in other way, discuss how the explain why a statement is valid, or how to prove it.
   1. Egypt
   2. Mesopotamia
   3. Hellenic (at, say 300BCE)
   4. China (at Liu Hui's time)
3. Problem 3 is here.
4. A man is carrying rice on a journey. He passes through three customs stations. At the first, he gives up 1/3 of his rice, at the second 1/5 of what was left, and at the third, 1/7 of what remains. After passing through all three customs stations, he has left 5 pounds of rice. How much did he have when he started? (This is on of the 246 problems on the Nine Chapters. Versions of this problem occur in later sources in various civilizations.)
5. There is a hole at the foot of a pillar nine hastas high, and a pet peacock standing on top of it. Seeing a snake returning to the hole at a distance from the pillar equal to three times its height, the peacock descends upon it slantwise. Say quickly, at how many hastas from the hole does the meeting of their two paths occur? (It is assumed here that the speed of the peacock and the snake are equal. This is a problem from the Lilavati)