Math 402: Non-Euclidean Geometry

Fall 2015

Instructor: Vesna Stojanoska


Syllabus

can be downloaded from here.

Note: the length of reflection papers should be 1-2 pages single spaced.


News

The final is comprehensive and will be held on December 14, 1:30-4:30pm in 217 Noyes.


Materials for completed exams

Here are some practice problems for the first midterm.

The practice problems for the second midterm.

Practice problems for the third midterm are here.


Assignments

Date due What to do
Mon 12/7 Reflection paper 5 is based on the following questions.
Fri 12/4 Homework 11 is here.
Mon, Wed 12/7-9 Reading. Review!
Wed, Fri 12/2-4 Reading. Chapters 7.2.2, 7.8, 8.3.
Mon 11/30 Reading. Chapter 8.4
Fri 11/13 Worksheet 7 is here.
Fri 11/13 Reading. Chapter 8.6.1.
Mon 11/30 Project 6 is 8.7 (project 12) from the book. New due date!!!
Fri 11/13 Homework 10. Recall the definition of the inverse of a point with respect to a circle, and prove that formula (8.4) in the book is correct. Then understand the proof of Lemma 8.8, and write it down in your own words. In addition, solve the following problems: 8.2.11, 8.2.14.
Worksheet from 11/6 is here.
Mon 11/9 Project 5. You should have already worked on Project 11 (Chapter 7.7) from the book. Now, recall what you did, then write a report and submit it.
Fri 11/6 Homework 9. The following problems: 3.5.6, 3.5.7, 3.5.8, 3.5.9, 8.2.1, 8.2.3.
Wed 11/4, Fri 11/6 Reading. Chapters 8.1, 8.2.
Mon 11/2 Reading. Chapter 3.5.
Mon 11/2 Reflection paper 4. Answer the questions of exercise 7.6.3.
Fri 10/30 Homework 8. The following 3 problems: 7.5.13, 7.6.1, 7.6.2.
Worksheet from 10/30 is here.
Wed 10/28, Fri 10/30 Reading. Chapter 7.5, 7.6
Mon 10/26 Project. Work out Project 7 (Section 5.5) and Project 11 (Section 7.7) from the book, but do not submit a report.
Worksheet from 10/9 is here.
Fri 10/16 Update: Homework 7 is now only consisting of 7.3.3, 7.3.5.
Fri 10/16 Reading. Chapter 7.5
Mon 10/12, Wed 10/14 Reading. Chapter 7.3
Mon 10/19 Project 4 is Project 10 (Chapter 7.4) from the book.
Wed 10/7, Fri 10/9 Reading. Chapters 3.4, 3.5, 5.6, 5.7.
Mon 10/5 Reading. Chapters 3.1,3.2.
Fri 10/9 Homework 6. The following 7 problems: 3.2.3, 3.2.5, 3.2.6, 5.7.3, 5.7.4, 5.7.5, 5.7.6.
Mon 10/12 Project 3 is Project 8 (Chapter 5.8) from the book.
Worksheet from Wednesday's lecture is here.
Mon 10/5 Reflection paper 3. Complete exercises 5.2.5, 5.3.1, 5.3.2, and 5.4.3. Discuss your solutions (non-mathematically).
Fri 10/2 Homework 5. The following 9 problems: 1.4.7, 5.1.1, 5.1.2, 5.1.4, 5.1.5, 5.2.11, 5.2.12, 5.3.5, 5.4.4.
Wed 09/30, Fri 10/2 Reading. Chapters 5.2, 5.3, 5.4.
Mon 09/28 Reading. Review in detail pages 24&25 (Ch 1.4), and read Chapter 5.1.
Mon 09/28 Project. Work on mini-project 7.2.2 from the book, but do not submit a report.
Wed 09/23 Worksheet from Monday's lecture is here.
Week of 09/21 Reading. Review and prepare for midterm.
Wed, Fri 09/16,18 Reading. Chapters 2.5, 2.7 (especially 2.7.1)
Wed, Fri 09/16,18 Worksheet from Monday's lecture is here.
Mon 09/21 Project report 2. Chapter 2.7: Circle inversion and orthogonality
Fri 09/18 Homework 4 is now complete.
Wed 09/16 Reading. Chapters 7.2, 7.3
Mon 09/14 Reading. Chapters 2.6, 7.1, and 7.2
Wed 09/09 Reading. Chapter 2.1, 2.2
Fri 09/11 Homework 3. Download assignment.
Mon 09/14 Reflection paper 2. Download assignment.
Wed 09/02 Reading. Appendix D, Chapter 2.1, and Wikipedia entry on projective planes
Fri 09/04 Homework 2. Download assignment.
Mon 08/31 Reading. Review all of Chapter 1, read Appendix D and Chapter 2.1
Wed 09/09 Project report 1. Do Project 2 (Chapter 1.7) as described in the book (i.e. the hyperbolic geometry model), then repeat for the spherical geometry model (File-> New-> Spherical). For the report, compare and contrast all three geometries (Euclidean, hyperbolic, and spherical).
Fri 08/28 Reading. Chapters 1.5, 1.6, Appendix A
Fri 08/28 Homework 1. Is the following axiomatic system consistent? If yes, give a model; if not, show why.

The undefined terms are points, and a line is defined as a subset of points.

Axiom 1. There are finite number of points.

Axiom 2. Any two different points belong to an exactly one line.

Axiom 3. Any two different lines have exactly one point in common.

Axiom 4. There exist four points such that any three of them do not belong to the same line.

Wed 08/26 Reading. Chapters 1.1, 1.2, 1.4
Wed 08/26 Tech. download and install Geometry explorer from here.
Fri 08/28 Homework 1. Exercises 1.4.3, 1.4.4, 1.4.5.
Mon 08/31 Reflection paper 1. Guiding questions: What is a straight line? How would you describe a straight line to an alien (or to a toddler)? Which properties of straight lines hold in every part of the universe, or even in a different universe? How can you check if something is a straight line, or if a ruler is straight? How can you construct something straight?

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