Math 420

Extended Essay #2

Due:  Friday, March 25.

Once again, you have several options for an extended essay.

I.    Over the past few weeks, we have discussed the development of Hellenistic mathematics, its transmission to the Islamic world, and its return to Europe.  We can consider this route by considering the history of some of the classic books of Hellenistic mathematics.

Pick one the three books

and write an essay (3 - 5 pages) on the story of one of these books starting  from its first writing and carrying it through to European times.  With Euclid, we should probably end the story with the first publication as a printed book.  With the Almagest we should probably end shortly after Copernicus.  With Diophantos' Arithmetic, we should follow it through roughly to the book that Fermat read.

II.    Another option is to expand on the classroom discussion on the movement of Hindu number representation and the algorithms for addition, subtraction, multiplication and division from India, through the Arabic world, and its re-introduction into Europe, primarily through the work of Leonardo of Pisa.  Track this development, including a discussion of the Arabic algorithm for multiplication (as one possibility), and the introduction of Liber Abaci and other works.  Berggren is a good source for Islamic mathematics.

III.    A final topic would be to explore why the Liber Abaci was so popular, what some of its competitors were, and why it took so long to for Arabic numerals to be adopted (they were not introduced into England until Recorde's book).