[Today’s class:  Logic puzzles activity,

Mesopotamian mathematics, including base 60 fractions, square roots and Pythagorean Theorem (one of these years: writing on modeling clay tablets with styli fashioned from sticks or chopsticks),

Introduction to ancient Chinese mathematics, including Chinese Counting Board activity,

Ancient Greek mathematics:  Thales’ Shadow Measurement activity (measuring heights of tall objects via similar triangles),

The Pythagoreans and their work with figurate numbers (activity),

Gauss sum formula]

Mathematics 115

Homework Assignment #8

Due Monday, January 21, 2002

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Prof. Beery's office hours this week:        Thursday 1/17   11 a.m.-12:30 p.m., 4-5 p.m.

Friday 1/18   2:30 - 4:30 p.m.

Monday 1/21   10:30 a.m.-12:30 p.m., 4-5 p.m.

and by appointment   Hentschke 203D, x3118

Tutorial session:  Sunday 1/20, 4 – 5 p.m., Hentschke 204 (Jody Cochrane)

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Read from the Mathematics of Ancient Egypt and Mesopotamia Section:

"Babylonian Mathematics" (pages 60-65, 75, and 76---especially pages 60-63,

75, and 76)

Do:    1.   According to the author, why were the ancient Mesopotamians able to develop

arithmetic and algebra more advanced than that of the ancient Egyptians?

2.            Describe (very briefly) the Mesopotamian (Babylonian) method of division.

3.            Explain the calculation  7(0;30) = 0;210 = 3;30  on page 62.  Show how to

convert these numbers to our numbers using fractions, not decimals.  (Hints:

The base is 60.  The semicolon  ;  acts like our decimal point.)

4.      For what is King Hammurabi I famous?

5.      Solve the following problem from an Old Babylonian (1900-1600 BCE) tablet:

Find the area of an isosceles trapezoid with sides of length 30 units and with

bases of lengths 14 and 50 units.  (Hint:  Pythagorean Theorem)

Diagram missing - sorry!

Read from the Mathematics of Ancient Greece Section:

"The Greeks" and "Thales of Miletus" (pages 397-398).

“Pythagorean Mathematics” (including the two paragraphs on Thales at the

top of page 88)

Do:    6.   Exercises 1, 2a, and 3 from Thales’ Shadow Measurement handout

7.      List the four subjects studied by the Pythagoreans.

8.      List the seven liberal arts.

9.      How was the Pythagorean motto, “Everything is number,” supported by

the Pythagoreans’ study of music?

10.    What could Pythagoras hear that no one else could hear?

11.    Find the 6th triangular number and the 6th square number.

12.    Find the 27th triangular number and the 27th square number.

Monday's class will begin at 1:15 p.m. and will end at the usual time.

Monday's quiz will be a 20-point quiz covering our work in class today and

On Monday, please bring scissors and a ruler.

Just for fun:       The first arrangement of numbers below is called a magic square, while

the second is called a diabolically magic square.  Why?

6    1    8                                   4     5   16      9

7   5   3                                 14    11     2      7

2    9    4                                   1      8   13    12

15    10     3      6

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