Homework

Assignments are due at the beginning of class on the day listed.

Online Homework Help: If you cannot attend office hours, you may also direct questions about homework and study questions to the FirstClassHelp website. Use descriptive titles on your posts.

August

Tuesday

Thursday

25	First Class Day

Read the course syllabus.
Read §1.1: Historical Background
HW 1: Email Introduction
Send me an email introducing yourself. Please give me some background on yourself, your academic experiences, and why you have enrolled in this course. I would like to get to know each of you and to help shape your experiences in this class to maximize your goals. My email address is oehrtman@math.asu.edu.

September

Tuesday

Thursday

1	Read §1.2: Axiomatic Systems and Their Properties Read §1.3: Finite Geometries Read §1.4: Axioms for Incidence Geometry

3	Read §2.1: Introduction HW 2: Axiomatic Systems §1.2 #5, 6, 7, 9, 13, 15, 24 §1.3 #4, 14, 15, 16, 26 §1.4 #1, 4, 6, 11

8	Read §2.2: Euclid's Geometry and Euclid's Elements Read §2.3: Modern Euclidean Geometries

10	Read §2.4: Hilbert's Axioms for Euclidean Geometry Read §2.5: Birkhoff's Axioms for Euclidean Geometry Read §2.6: The SMSG Postulates for Euclidean Geometry HW 3: Euclid's Triangle Propositions - Part 1 (You'll need to reference this website on Euclid's Elements and use GeoGebra.)

15	Read §2.7: Non-Euclidean Geometries

17	Read §3.1: Introduction Read §3.2: Preliminary Notions Read §3.3: Congruence Conditions HW 4: Euclid's Triangle Propositions - Part 2

22	Read §3.4: The Place of Parallels

24	Read §3.5: The Saccheri-Legendre Theorem Read §3.6: The Search for a Rectangle HW 5: SMSG Triangle Propositions §3.2 #1, 2, 5, 8, 9, 12, 13 §3.3 #2, 6, 8

29	Read §4.1: Introduction Read §4.2: The Parallel Postulate and Some Implications

October

Tuesday

Thursday

1	Read §4.9: Euclidean Constructions HW 6: Parallel Lines §3.4 #1, 2, 4, 6 or 7, 11 §3.5 #3 §3.6 #1, 28, 30 §4.2 #1, 2, 8, 9, 10

6	Euclidean Constructions Read §4.3: Congruence and Area Read §4.4: Similarity

Read §4.5: Some Results Concerning Circles
HW 7: Euclidean Constructions

§4.9 # 2, 4, 6, 8, 25
Create responses to the following in GeoGebra (using only the "postulate tools"): §4.9 #16, 21
Create the constructions in GeoGebra for the following of Euclid's propositions (using only the "postulate tools"). Use decorations to illustrate every congruence mentioned in Euclid's construction and proof: Propositions 22, 23, 31, 46

13	Exam 1: See Outline Here

15	Read §5.1: Introduction Read §5.3: Transformational Geometry Study for a quiz on §5.3.

20	Reread §5.3: Transformational Geometry

22	Read §6.1: Introduction Read §6.2: A Return to Neutral Geometry: The Angle of Parallelism HW 8: Transformational Geometry §5.3 #6, 7, 8, 13, 18, 19, 20, 21, 22

27	Read §6.3: The Hyperbolic Parallel Postulate Read §6.6: Showing Consistency: A Model for Hyperbolic Geometry

29	Read §5.5: Inversion HW 9: Hyperbolic Geometry

November

Tuesday

Thursday

3	Read §6.4: Hyperbolic Results Concerning Polygons

5	Read §6.5: Area in Hyperbolic Geometry HW 10: Transformations and Hyperbolic Geometry (You will also need the files SAS Blank.ggb and ASA Blank.ggb)

10	Read §6.7: Classifying Theorems

12	Read §6.8: Elliptic Geometry: A Geometry with No Parallels HW 11: Area and Holonomy

17	Read §6.9: Geometry in the Real World

19	Exam 2: See Outline Here

24	Read: Differential Geometry Handout 1 HW 12: Spherical and Elliptic Geometry §6.7 #7, 12, 13, 15, 17, 22 (Construct counterexamples in NonEuclid and verify with the measurement tools.) §6.8 #1, 2, 4

26	Thanksgiving

December

Tuesday

Thursday

1	Read: Differential Geometry Handout 2

3	HW 13: Differential Geometry Homework (due on the 3rd if you want your work graded and returned before the final) HW 13 Solutions

8	Last Class Day HW 13: Differential Geometry Homework HW 13 Solutions

15	Final Exam 12:10pm - 2:00pm