[Today’s class:  Ancient Egyptian mathematics, including

multiplication and division by doubling (and halving), and

unit fractions, including Horus eye fractions, looking for patterns, and fair division of loaves of bread using unit fractions (use small loaves of cake-like bread or just pencil and paper)]

Mathematics 115

Homework Assignment #6

Due Wednesday, January 16, 2002

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Prof. Beery's office hours this week:            Tuesday 1/15   10:30 a.m.-12:30 p.m., 4-5 p.m.

Wednesday 1/16   11 a.m.-12:30 p.m., 4-5 p.m.

Thursday 1/17   11 a.m.-12:30 p.m., 4-5 p.m.

Friday 1/18   2:30 - 4:30 p.m.

and by appointment   Hentschke 203D, x3118

Tutorial session:  Day: ____________, Time: ____________, Place: ______________

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"Prime Numbers"

"Sources of Information on Ancient Egyptian Mathematics"

"Mathematics in Early Civilizations" (pages 31-39: "The Rhind Papyrus"

and "Egyptian Arithmetic")

Do:    1.   What are the distinguishing characteristics of a hydraulic society?  In answering

this question, be sure to say what "hydraulic" means in this context, what the

main occupation of the people in a hydraulic society is, what the political

structure of such a society usually is, and what sort of mathematics such a

society usually produces.

2.   In "Hydraulic Societies," author Frank Swetz claims that the Greek society

that was emerging along the shores of the eastern Mediterranean Sea in about

600 BCE had a different approach to mathematics from those of previous

societies (specifically, the Mesopotamian and Egyptian civilizations).

How was the Greeks' approach different from that of the Egyptians?

Give at least three possible reasons for their new approach.

3.   In "Prime Numbers," author James Ritter points out two differences between

Mesopotamian and Egyptian writing and numbers.  Name them.

4.   Who were the "mathematicians" of early Mesopotamian and Egyptian society?

What were their jobs?  How were they trained?

5.   What famous object was the key to reading ancient Egyptian monuments and

documents in modern times?  What was the easy (known) part of this key?

If French Emperor Napoleon Bonaparte found this key, how did it end up

in the British Museum?  (And why hasn't it been returned to Egypt?!)

6.   Use Egyptian doubling to compute (a) 18 x 25, (b) 26 x 33, (c) 21 x 85, and

(d) 59 x 105.

7.   Use Egyptian division to divide  174  by  6, and to divide  124  by  16.

8.   Write the fractions  3/10, 7/10, and 9/10  as sums of distinct unit fractions

and, if you like, the fraction 2/3 (as the Egyptians did).

Wednesday's quiz (20 points) covers today’s class and Assignment #6 (above).

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