Geometry for Teachers

MTH 623 Section 48923 Fall 2019

Monday & Wednesday, 4:40 pm - 6:20 pm, Room 4S-217

Report Topics and Guidelines

1. Report counts for 20% of your course grade.


2. Report is due by 10 pm on Friday Dec 6th . Please submit the report by email as an attachment in pdf format only. Please send email to abhijit@math.csi.cuny.edu.


3. The topics are listed below and will be offered on a first come first serve basis. If applicable, please pick a topic different from the topic of your previous report in a Geometry class.


4. The report can either be done individually or in collaboration with one other student from the class. Please email me or inform me about the topic and your co-author latest by Friday Nov 15th.


5. 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.


6. 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.


7. 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.


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

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• Report Topic #1: Summarize the book Flatland
  Please collect the book from me.


• Report Topic #2: Cartography and projections of $S^2$.
  Read about the following projections and their applications to maps and use them in your report.
  1. Mercator projection
  2. Gnomonic projection
  3. Gall-Peters projection (wikipedia)
  4. West Wing excerpt about map projections


• Report Topic #3: Models for the hyperbolic plane
  
  1. Poincase disk model #1
  2. Poincare disk model #2


• Report Topic #4: Inversions
  Chapter 7 of the text book.


• Report Topic #5: The 17 wallpaper symmetry groups of the plane
  
  1. Sections 6.7 of the book.
  2. Book: The symmetry of things (Please collect from me)
  
  
• Report Topic #6: Finite Geometries
  
  1. Finite Geometries #1
  2. Finite Geometries #2
  3. Finite Geometries #3
  
  
• Report Topic #7: Symmetry in Space
  Chapter 8 of textbook.
  
  
• Report Topic #8: Planar graphs and Eulers Theorem
  Section 10.1, 10.4 of text book.


• Report Topic #9: Surfaces
  Sections 11.1 - 11.3 of the text book.


• Report Topic #10: Knots, links and lableings
  Section 12.1, 12.2 of text book.


• Report Topic #11: Knots, links and the Jones polynomial
  Section 12.1, 12.3 of text book.


• Report Topic #12: Hilbert's 3rd problem and Scissors Congruence
  
  1. Slides
  2. Notes by Efton Park
  3. What is a scissors congruence by D. L. Dupont