Assignment 5b:

Math in the Islamic World: Overview

 

Due:

-Annandale- Thursday, February 28st

-Fishkill- Friday, March 8st

 

Quadrivium

Mathematics and Metaphysics

in the Premodern World

 


 

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 12th 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. 

1

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)

1

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

 

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.]     x2 + 10x = 39

 

-From Suzuki, p. 89: Figure out what the biblical value for was using the qavah/qava ratio.

     3(111/106) = 3.141509 43...                   3(111/106) – = –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 .]

                From Suzuki, p. 88: "Three and one-seventh" or  is the standard rational approximation of .  It is a very good approximation.  Can you come up with a more accurate rational approximation for ?  ...meaning, find a rational fraction (whole number numerator and denominator) that is a more accurate approximation of .  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:

 

IOT-Muslim Spain

 

IOT-Pi-

 

IOT-Early Islamic Maths

 

IOT-Prime Numbers

 

RadioLab-Numbers

 

RadioLab-For the Love of Numbers

 

IOT-Indian Maths

 

IOT-Zero