Foundations of Geometry, Second Edition by Gerard A. Venema,Please keep a portfolio of your written work. Be prepared to discuss your assignment solutions in class. Show faculty your completed assignments at the end of the week.
Prentice Hall, 2012 ISBN: 978 0 13 602058 5
In general, be sure you do the chapter reading before class and be prepared to ask questions and discuss the ideas and proofs in the chapter. You don't need to complete the problems before class because we'll work on them in class. It will help to read and understand what the problems are asking before you come to class.
Class Topic Assignment Reading and Problems
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1 Euclid's Elements Read Chapter 1 and Appendix A
Do problems:
Ch 1 Sec 1.6: 3,6,8, *(7,9,10) * means extra credit
Note: Problem 3 is an explanation not a real proof
(because we don't know what the ancient systems were)
Additional problems:
(a) Write up Euclid Proposition 1 as a "two-column" proof
using the outline given in class (thm stmt, givens, show, idea, proof)
(b) Find the propositions of Euclid that correspond to each
of the three constructions of problem 1.6 in the text and
give the two-column proofs for each.
2 Incidence Geometry Read Chapter 2 Sections 2.1 to 2.4
& Models Ch 2 Sec 2.4: 1-8,11,12, *(9,10)
3 Logic & Proofs Read Chapter 2 Sections 2.5, 2.6
Ch 2 Sec 2.5: 1-12
4 Numbers & Proofs Read Chapter 2 Section 2.6 and Appendix E
Ch 2 Sec 2.6: 1-4
Additional problems:
(a) Convert the proof of Theorem 2.6.2 p33 to a two-column proof
(b) Prove that the square of an odd positive integer is always odd.
(c) Prove that if a^2 is even then a must be even.
Present portfolio work for Chapter 1,2
5 Plane Geometry Read Chapter 3 Sections 3.1 to 3.3
Ch 3 Sec 3.2: 1,2,3,5,6,7,17,19,21, *(15,18)
Ch 3 Sec 3.3: 5, *(3,4)
6 Plane Geometry Read chapter 3 Sections 3.4 to 3.7
Ch 3 Sec 3.4: 1
Ch 3 Sec 3.5: 2,4,5, *(3)
Ch 3 Sec 3.6: 1
Ch 3 Sec 3.7: 1,2
7 Finish portfolio work for Chapter 1,2,3
8 Neutral Geometry Read chapter 4.1-4.4.
Ch 4 Sec 4.1: 1,2
Ch 4 Sec 4.2: 1,4,5
Ch 4 Sec 4.3: 2, *(7)
Ch 4 Sec 4.4: 1,2
9 Neutral Geometry Read chapter 4.5-4.9.
Ch 4 Sec 4.5: 1,2
Ch 4 Sec 4.6: 1
Ch 4 Sec 4.7: 1, *(2)
Ch 4 Sec 4.8: 5, 8 (choose parts to do for 5,8)
Present portfolio work for Chapters 1,2,3,4
10 Euclidean Geometry Read chapter 5.1-5.4.
Ch 5 Sec 5.1: 2
Ch 5 Sec 5.3: 2 *(1,3) You may substutute * problem
Ch 5 Sec 5.4: 3 *(1,2) You may substutute * problem
11 Hyperbolic Geometry Read chapter 6.1-6.3, 6.6, 6.9
Ch 5 Sec 6.1: 2,3
Ch 5 Sec 6.2: 1,2
Write a paper summarizing the key concepts of
hyperbolic geometry along with the corresponding
results presented in sections 6.1, 6.2, 6.3, 6.6
of the textbook. Write the story you want to tell
about hyperbolic geometry to your students.
Four pages typed (est).
12 Transformations Read chapter 10.1-10.5
All Portfolio Work Due
Submit portfolio work for Chapters 1-6
* Extra credit problems