[Today’s class: Sieve of Eratosthenes activity,

Heron, Diophantus, Hypatia,

Geometric algebra, including algebraic identities, square root computation in China, one more proof of Pythagorean Theorem, and completing the square,

Mathematics of Middle Ages, especially of Arab Empire]

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**Homework Assignment #10**

*Due **Thursday, January 24, 2002*

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__Prof.__ __Beery's__ __office__ __hours__: ** **Wednesday
1/23 4 – 5 p.m. (Sorry!)

Thursday 1/24 11 a.m.-12:30 p.m., 4-5 p.m.

Friday 1/25 2:30 - 4:30 p.m.

and by appointment Hentschke 203D, x3118

__Tutorial__ __sessions__: Thursday 1/24 morning, 11 a.m., Hentschke
202 (Sasha)

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__Read__: "Heron's Formula for Triangular Area" (Eratosthenes,
Apollonius, Heron,

Ptolemy, Mohammed ibn Musa al-Khowarizmi, Tabit ibn Qorra)

"Hypatia" (These are the last two readings in the Math of Ancient Greece section.)

"Cardano and the Solution of the Cubic" (Mathematics of Europe section)

__Do__: **A.** Algebra in Classical Greece worksheet
(handout from class)

**B.** Algebra
in the Middle Ages worksheet (handout from class)

**C.** Solve
for x in the equation x^{2} + 6x = 16 by completing
the square as shown

in class today.
Use Steps 1 - 4 as demonstrated in class. You should get __two__

solutions, x = -8
and x = 2. Then __draw__ __a__ __picture__ of the completed square

corresponding to the problem (as shown in class).

**D.** Answer
the following questions about "Heron's Formula for Triangular Area."

1. Use
the quadratic formula to solve the quadratic equation 3x^{2} + 2x - 5 = 0.

(Hint: See page 130!)

2. How did "Dark Age" Europeans eventually acquire the mathematical knowledge

of ancient Greece and of the Arab empire? Be sure to include what author

William Dunham describes as the more significant conduit for this knowledge

as well as the less significant conduit.

**E.** Answer
the following question about "Cardano and the Solution of the Cubic."

Why did fifteenth and sixteenth century Italian mathematicians keep their

mathematical discoveries secret?

**Thursday's quiz** will be a 20-point quiz covering activities from
today’s (Wednesday’s) class, and the reading and homework from this assignment
(Assignment #10). This includes being able to tell me stories about Hypatia,
and about Cardano and Tartaglia.

For **Thursday's class,**
please bring a **ruler.**

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