Report Topics and Guidelines

  1. The report counts for 20% of your course grade.

  2. The report is due in class on Wednesday Dec 7th. You may submit the report on paper, or by email as an attachment in pdf format only.

  3. Everyone needs to pick a different topic for the report. Some suggested topics are listed below. Please email me if you would like to pick one of the suggested topics. If you would like to choose your own topic, come and discuss it with me first.

  4. The report should be 4 to 5 pages long , single spaced in 11 or 12 point font and should be typed in a word processor of your choice or in Latex (math typesetting program). Figures can be hand drawn if required.

  5. You are encouraged to find resources and references other than those listed below. Please list all the references you use including that of the figures copied from the internet or elsewhere on a separate page, which is in addition to the 4 - 5 pages of the report.

  6. The report should be a math paper with theorems, proofs, formulas and figures as needed and will be graded as such. It should explains the topic at hand sufficiently well and in your own words. Plagiarism from any source will not be tolerated.

  7. I encourage you to discuss your report with me before finalizing and submitting it.

Report Topics

  1. Summarize the book Flatland

    • Check with me to see if I have a copy.

  2. Cartography and projections of \(S^2\).

    Read about the following projections and their applications to maps and use them in your report.

  3. Models for the hyperbolic plane

  4. Inversions

    • Chapter 7 of the text book.

  5. The 17 wallpaper symmetry groups of the plane

    • Sections 6.7 of the book.
    • Book: The symmetry of things (check with me to see if I have a copy).

  6. Finite Geometries

  7. Symmetry in Space

    • Chapter 8 of textbook.

  8. Planar graphs and Eulers Theorem

    • Section 10.1, 10.4 of text book.
    • Book: Proofs and Refutations

  9. Surfaces

    • Sections 11.1 - 11.3 of the text book.

  10. Knots, links and lableings

    • Section 12.1, 12.2 of text book.

  11. Knots, links and the Jones polynomial

    • Section 12.1, 12.3 of text book.

  12. Hilbert's 3rd problem and Scissors Congruence