Guidelines for papers

You will prepare two research papers for this course:

• a paper due January 23, that explores the heritage of Euclid's Elements; and
• a paper due April 15 that investigates a geometrical topic of interest to you.

• The paper should present a comprehensively researched discussion of the stated topic. (50%)
• It should be presented in a clear and coherent writing style, using correct spelling, proper pronunciation and good grammar. (15%)
• It should contain a bibliography with at least three sources including at least three print-published (not Web) sources, it should make appropriate use of direct quotations, and should include in-text citations (as either footnotes or endnotes). (25%)
• It is to be 5-8 pages long, typed or word-processed, double-spaced in a standard 10 or 12 point font with 1 inch margins.  Include a final blank page for my comments. (10%)

Read the following:

• Euclid's Elements, Book I.  This link is to the celebrated web version of the Elements prepared by David Joyce of Clark University.
• Euclid and the Elements, Sections 4.1 - 4.2, The History of Mathematics: an introduction, 5th ed., McGraw-Hill, 2002, pp. 135 - 152.

"Why and how we should correct the mistakes of Euclid," Mathematics Teacher 53 (1960) 576 - 581. In this paper, Daus addresses the School Mathematics Study Group, a group of college and university mathematicians, teachers of mathematics at all levels, experts in education, and representatives of science and technology, who developed a K-12 mathematics curriculum in the early 1960s (best known today as "the New Math").

Your paper should address the following six questions:

• What are Euclid's Elements?  Who is Euclid, and why did he write the Elements?
• Give evidence for the profound influence of this work on mathematics and geometry in particular.
• Discuss the importance of the many results compiled by Euclid in this encyclopedic compendium of ancient Greek geometry, as well as the axiomatic style in which he presents the results.
• Why was the fifth postulate of Book I of the Elements so carefully studied by centuries of geometers?
• Describe some of the "mistakes" that Daus accuses Euclid of having made and some of his suggestions for correcting them in designing school curricula.
• Do you think that Euclid's geometry as presented in the Elements would make a suitable high school geometry curriculum today?  Why or why not?

I urge you to make use of the library staff to help you find resources for your research; but check with me if you have persistent difficulties tracking something down.