Math 5335 Geometry I

Fall 2015

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Syllabus & Course Information

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• Syllabus (last revised on 09/08/15)

Office Hours: Tuesday, 11-12:30 and Friday, 1:30-2:20 in Vincent 4

Professor Joel Roberts, who has taught this course multiple times, has posted a good explanation of how our approach to Geometry will be somewhat different than other courses. Please read it during the first week of the class.

You can download the worksheets we used at various times in class.

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Related Links

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• Gradebook (on Moodle)
• GeoGebra
• Motorcycle movie about Geodesics
• Isometries and Symmetry
  • Freize Patterns
  • Wallpaper Groups
  • Use of Isometries in Escher's Tessellations
  • Escher's Horsemen (1946) Can you spot the glide reflections?
• Encyclopedia of Triangle Centers
• The Eyeballing Game
• Achieving the Unachievable, about the mathematicians who reverse-engineered Escher's "Print Gallery."
• Stereographic projection of the sphere onto the plane, which is a conformal map. If you do "reverse" or "inverse" stereographic projection, lines one the plane are mapped to circles through the north pole, which corresponds to the "point at infinity" on each line. See this example.
• Penrose Tiles
• Geometry Games. You can download the tic-tac-toe game we used in class (Torus Games) or the fly-throughs of the possible shapes of the universe (Curved Spaces; the 3-torus is the "box").
• Origami TED Talk

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Lecture Schedule & Homework Assignments

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Week of	Reading	Homework	Due	Solutions
9/7	Syllabus. Section 1 of 5335 description by Prof. Roberts.	Lab Assignment #0	W 9/16
9/14	Sections 1.1-1.3 Review of Linear Systems of Eqns	Problems 1.5, 1.21(i,iii,v), 1.28, 1.35, 1.41, 1.45 (Hint: don't use coordinates. Write the length in terms of dot products and distribute!)	W 9/23	pdf
9/21	Sections 1-4--1.7, 2.1	Lab Assignment #1	W 9/30
9/28	Chapter 2	Problems 2.8, 2.17, 2.18, 2.24, 2.35, 2.36	W 9/23	pdf
10/5	End of Chapter 2 and 3.1, 3.2 Exam Review	Lab Assignment #2	W 10/14
10/12	Parts of Chapter 3 (follow class notes instead)	3.12, 3.13 (do together as one problem; simplify both answers to form in back of the book for 3.12), 3.16, 3.17, 3.23(i,ii,iv)	W 10/21	pdf
10/19	Rest of Chapter 3 / class notes Reflection Example	Lab Assignment #3	W 10/28
10/26	Chapter 4 Chapter 5 (start)	3.57, (4.2, 4.3 together as one problem), 5.4, 5.6 (you may use Prop 5.19), 5.13, 5.20. For Chapter 5 problems you may use any valid triangle congruence theorem: SSS, SAS, ASA, AAS	W 11/4	pdf
11/2	Rest of Chapter 5 Section 6.1	Lab Assignment #4	W 11/11
11/9	Chapter 6 Section 7.1 Exam Review	Lab Assignment #5	W 11/18
11/16	Chapter 7	Problems 7.4, 7.5, 7.13, 7.14(i,iv)	W 11/25	pdf
11/16	Chapter 8	Problems 8.23, 8.24, 8.25 Extra credit problem: Hand in a complete solution to the following problem by 12/4/10 at 2:30pm in my mailbox for five extra credit points: Find and prove the formula for the area of a triangle on a sphere of radius r. Also solve the formula for the sum of the angles. Here's a brief overview of spherical geometry for those who missed the relevant material on 11/25. You might prefer this page for finding the area of a lune. You should explain that area formula as part of your solution.	W 12/2	pdf
11/30	Chapter 9 (Except areas of triangles)	Lab Assignment #6	W 12/9
12/7	Chapter 9	Work on the Take-home Final Exam	M 12/21
12/14	Chapter 10	Work on the Take-home Final Exam	M 12/21

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Exam Info

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• Exam 1 (10/14/15): Exam Review
• Exam 2 (11/18/15): Exam Review

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Exam Gradelines

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Grade	Exam 1	Exam 2	Final
A	90	90	87
B	80	80	75
C	65	60	60
D	50	50	50

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