[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*

* *

_______________________________________________________________________

__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)

_______________________________________________________________________

__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 6^{th} triangular number and the 6^{th} square
number.

12.
Find the 27^{th} triangular number and the 27^{th} 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

Assignment #8 (reading and homework).

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