Assignment 5b: Math in the Islamic World: Overview Due: -Annandale- Thursday,
February 28^{st} -Fishkill- Friday, March 8^{st}
Quadrivium Mathematics and Metaphysics in the Premodern World |
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Read the following: |
folios |
Grant, Edward, ed. A Source Book in
Medieval Science. -Ch-7. [pp. 35-38] Gerard of Cremona (ca.
1114-1187): Arabic to Latin Translations. [Part of a previous handout.] This is just to give you an idea of
the scientific tradition in Arabic.
It was highly developed in the 12^{th} century. The influence of Arabic texts
(translated into Latin) is often cited as one of the main generators of the Renaissance
in Europe. The Renaissance can be
seen not as a rebirth, but as a discovery of Arabic/Islamic natural
philosophy, which not only built on Greek natural philosophy, but created a
natural philosophy that was commensurate with monotheism. |
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Katz, Victor J. ed. Sourcebook
in the Mathematics of Medieval Europe and North Africa. Princeton
University Press, 2016. -pp. 381-385: Islamic Mathematics
-introduction by Berggren.
[Contained in a previous handout.] |
1.3 |
Berggren, J. L. Episodes
in the Mathematics of Medieval Islam. New York. Springer. 2000 -pp. 6-9: Al Khwarizmi (ca. 780-ca.850) |
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Suzuki, Jeff. Mathematics in Historical Context. Mathematical Association of
America. 2009. -86-88 : Al Khwarizmi (ca. 780-ca.850) -88-89: Biblical Value of ¹ |
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To do: (Just be prepared to discuss. Nothing official to turn in.)
-From Berggren reading,
p8: Figure out al-Biruni's method
for determining the "measure of the length of one degree along the
meridian." You might have
to look up some terminology and do a little math. Compare al-Biruni's length with the
modern value. What was the
circumference of al-Biruni's earth?
-From Suzuki, p. 87: Read over
the block quote that starts, "One square, and ten roots..." Figure out the problem. Once you write down the various numbers
you might see how they all fit together.
[Hint: It's a quadratic.]
x^{2} + 10x
= 39
-From Suzuki, p. 89: Figure
out what the biblical value for ¹ was using the qavah/qava ratio.
3(111/106) = 3.141509
43...
3(111/106) – ¹ = –0.0000832...
Extra Credit: [Submit your
answer on paper with a clear explanation of method and result. More credit will be given if you do some
research on the topic... rational approximations of ¹.]
From Suzuki, p. 88: "Three and one-seventh" or is the standard rational approximation of
¹. It is a very good
approximation. Can you come up with
a more accurate rational approximation for ¹? ...meaning, find a rational fraction
(whole number numerator and denominator) that is a more accurate approximation
of ¹. Limit yourself to a
denominator lower than 500. Don't
look it up until after you have come up with a method and a fraction. Figure it out using only your brain.
Topical Podcasts:
RadioLab-For
the Love of Numbers