[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]
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 x2 + 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 3x2 + 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.