• Papers - The Process
• General Notes on Class Papers
• Selected References - Euclidean Geometry Paper
• Selected References - Non-Euclidean Geometry Paper
• Good Geometry Internet Sites
• Some Previous Paper Topics 1996-present

• Writing Expository Mathematics
• UMKC Writing Center
• UMKC Writing Across the Curriculum

• Written Outline, including your topic and a broad plan for the paper. Choose something you like! Be prepared to verbally explain to me (and maybe the class too) what you think your paper will cover. Include a list of at least 3 references you are looking at. Each student must have a different topic. Try to use original sources as much as possible, i.e., "Learn from the Masters!" Look at the references and bibliographies of your sources for further related sources! This is detective work; follow the clues, stick to the truth.

• Many Drafts improves the paper immeasurably. The First Draft Deadline in any case must be met. There will be a grade penalty if no First Draft is received by that date. A Draft should be at least half to three-quarters of the paper, in draft form of course. Type, please. Draw or write by hand any mathematics or pictures if necessary. Don't give a draft "for show". If there's nothing there, it is not acceptable.

• Previous Drafts. Always return the previous marked-up draft with the current draft, so I can recognize changes.

• Final Paper. See below for style, presentation, Title page, Reference page, 10+ internal pages, 10 or 12 pt font, 1 inch margins, etc.

• This semester you will be required to write a 10-page paper. These are "internal" pages, not including the title and bibliography pages. Due dates will be set in class.

• For the paper you will turn in at least one DRAFT, and then later the PAPER. The draft will not be graded, but I will return it to you promptly with written comments, and discuss these with you verbally in class. More than one DRAFT is highly recommended.

• All topics must be approved by me beforehand, and each person must have a different topic. The paper must cover a Euclidean Geometry or Non-Euclidean Geometry topic. Try to find a topic of particular interest to yourself.

• A paper must have a carefully explicated proof somewhere in it, possibly several. This will depend on your topic, of course; some papers will consist entirely of one "classic" proof, others will contain a series of smaller proofs. Discuss this with me.

• The papers should be roughly 60% (or more) mathematics and 40% (or less) English. The English parts must be typed with a word-processor. The mathematics portions can be typed using various programs/features (For instance, the Equation Editor in MS WORD, Math Type, Scientific Notebook, etc.). Diagrams or pictures, can be hand-written or drawn if needed. The notation of the Greenberg text, and this course, should be the notation you use in your papers, and should otherwise be standard. [Ask me if you have doubts.]

• I expect a Title page (title, name, course, date) and a Bibliography page as the last page. There must be at least 10 additional internal pages. Within your paper please refer to your numbered Bibliography references by numbers within square brackets, such as: [8] or, [17, p.242]. Book citations always require page references.

• Your paper should be double-spaced, with 1 inch (or less) margins. Your font should be no larger than 12 point.

• The Linda Hall Library of Science, Engineering, and Technology is a major resource. Use it, in addition to UMKC's Miller Nichols Library. Also, consider the Internet, but be highly critical of the information you find. Always confirm it in printed references. Use very few internet references in your paper.

• If you are looking for paper ideas, look at the books below. (Please avoid other books, especially textbooks. I have chosen these below as some of the best references to look at.) Also, Greenberg has Major Exercises and Projects at the end of chapters, two Appendices, a Suggested Further Reading page, and the Bibliography at the end of the book. Look ahead in the text too. Do not limit yourself to what we cover in class.

• The Trisection Problem, Robert C. Yates, NCTM Classics in Mathematics Education, 1971.
• The Pythagorean Proposition, Elisha Scott Loomis, NCTM Classics in Mathematics Education, 1972.
• 100 Great Problems of Elementary Mathematics, Their History and Solution, Heinrich Dorrie, Trans. by David Antin, Dover, 1965.
• Classics of Mathematics, ed. Ronald Calinger, Prentice Hall, 1995.
• Foundations of Geometry, David Hilbert, Open Court Pub. Co., 1971.
• Archimedes, E. J. Dijksterhuis, Princeton Univ. Press, 1987.
• Archimedes: What Did He Do Besides Cry Eureka?, Sherman Stein, Mathematical Association of America, 1999.
• The Works of Archimedes, with the Method…, Thomas L. Heath, Dover, 1897.
• Episodes in the Mathematics of Medieval Islam, J. L. Berggren, Springer Verlag, 1986.
• A Mathematical History of the Golden Number, Roger Herz-Fischler, Dover, 1987.
• Journey Through Genius: The Great Theorems of Mathematics, William Dunham, Penguin Books, 1990.
• A History of Mathematics: An Introduction, 2^nd Ed., Victor J. Katz, Addison Wesley, 1998.
• A Source Book in Mathematics, David Eugene Smith, Dover, 1959.
• The Penguin Dictionary of Curious and Interesting Geometry, David Wells, Penguin Books, 1991.
• Elementary Geometry from an Advanced Standpoint, 3^rd Ed, Edwin E. Moise, Addison Wesley, 1990.
• Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Ross Honsberger, Mathematical Association of America, 1995.
• The Ancient Tradition of Geometric Problems, Wilbur Richard Knorr, Dover, 1986.
• Euclid, the Thirteen Books of the Elements, vols 1,2,3, trans. by Thomas L. Heath, Dover, 1956.
• Pi: A Source Book, Berggren, Borwein, and Borwein, Springer Verlag, 1997.
• What is Mathematics?, Richard Courant and Herbert Robbins, Oxford Univ. Press, 1941.
• The Morley Trisector Theorem, Cletus O. Oakley and Justine C. Baker, American Mathematical Monthly, Nov. 1978, pp. 737-745.
• Euclidean and Non-Euclidean Geometries, Development and History, 3^rd Ed, Marvin Jay Greenberg, W. H. Freeman, 1993.

Oliver Byrne's 1847 Edition of Euclid (Books 1-6) in colored diagrams
www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.html

Euclid's Elements (with live Java diagrams)
http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

The Visual Elements of Euclid (Books 1-6, each proposition broken down into a series of colored graphics)
http://www.visual-euclid.org

Archimedes Home Page
www.mcs.drexel.edu/~crorres/Archimedes/contents.html

Flatland - The classic little book - Tom Banchoff's site at Brown University
www.math.brown.edu/~banchoff/gc/Flatland/

Flatland – The classic little book - another version
www.alcyone.com/max/lit/flatland/

San Gaku – Japanese Temple Geometry
www.wasan.jp/english/

MacTutor History of Mathematics Archive
www-history.mcs.st-and.ac.uk/history/

The Math Forum
http://mathforum.org/

The University Libraries at UMKC
www.umkc.edu/lib/

Linda Hall Library of Science, Engineering, and Technology
www.lhl.lib.mo.us

Poincare Draw
http://persweb.wabash.edu/facstaff/footer/PDraw/PDraw.htm

The Math Forum - Non-Euclidean Geometry
http://mathforum.org/library/topics/noneuclid_g/

The Math Forum - Poincare Disk with Geometer's Sketchpad
http://mathforum.org/sketchpad/gsp.gallery/poincare/poincare.html

Andy Bennett at KSU - Poincare Plane Java applets
www.math.ksu.edu/math572/hyp.html

Center for Scientific Computing (Finland) Mathematical Topics: Hyperbolic Geometry
www.csc.fi/math_topics/Movies/HG.html

The Geometry Center – Univ. of Minnesota [This site may now be closed.]
www.geom.umn.edu/java/triangle-area/

Hyperbolic Geometry - The Open University, England - with Cabri Geometry software
http://mcs.open.ac.uk/tcl2/nonE/nonE.html

Some Explorations in the Poincare Model of the Hyperbolic Plane, by Kevin M. Pilgrim, University of Missouri - Rolla
www.umr.edu/~pilgrim/Teaching/Math330W00/explorations.html