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MATH3560 Mid-Session Test
Due Date: Midnight Friday 19th March 2021
Instructions
• Use only those methods available to Mesopotamian scribes. You are per-
mitted to use variables x, y, z and modern mathematical terms to describe
your working.
• You are required to show your working, except for the multiplication steps.
• Leading or trailing zeros may be used to indicate magnitude.
Questions
1. A rectangular throne room has base 40 ninda, width 10 ninda and height
8 ninda. What is the distance between opposite points in the room (i.e.
from one corner of the floor to the opposite corner on the ceiling)?
2. You borrow 1 gur of grain from the National Assyrian Bank and pay 20
percent interest, compounded annually. If you make annual repayments
of 13 = 0 : 20 gur, how long (to the nearest month) will it take for you to
owe 23 = 0 : 40 gur of grain?
3. Find a two-digit approximation for
√
3.
4. A canal (Figure 1). The length 30, upper width 25, lower width 18 and
height 14 (all units are ninda). The canal is made deeper and now has a
total capacity of 3 : 20 : 00 cubic ninda. How much deeper is the canal?
What is the new lower width?
5. Explain the following question and answer.
Question: A little canal (Figure 2). The length 20. On the first day a
depth of 4 was dug and the lower width was 6. On the second day,
more was dug and the lower width became 12 (all units are ninda).
A total of 1 : 06 : 00 cubic ninda was extracted. What is the upper
width w of the little canal?
Figure 1: Cross section of the canal.
Answer: You, with your doing. 3, the reciprocal of 20, to volume raise.
The surface 3 : 18 you see. 15, the reciprocal of 4, to 3 : 18 raise.
49 : 30 you see. 49 : 30 repeat, 1 : 39 you see. The two widths, add.
18 you see. To 1 : 39 raise, 29 : 42 you see. May your head hold.
49 : 30 square, 40 : 50 : 15 you see. From 40 : 50 : 15 tear out the
29 : 42 which your head was holding. 11 : 08 : 15 you see. 12 square,
2 : 44 you see. To 11 : 08 : 15 add, 13 : 32 : 15 you see. What is the
square root of 13 : 32 : 15? 28 : 30 is the square root. From 49 : 30
tear out 28 : 30. 21 you see. 21, the upper width. The procedure.
Figure 2: Cross section of the little canal.