Eucidean and Non-Euclidean Geometry

Fall 2006, Math 475/675
[ Lectures and homework | Graded assignments | Homework solutions]

Textbook:  Marvin Jay Greenberg - "Euclidean and Non-Euclidean Geometries", 3-rd edition. Published by Freeman and Co., ISBN: 0-7167-2446-4.

Assessment: The final grade for the course will be determined as follows:
 

Practice Homework: The purpose of the exercises from the practice homework is to give you a chance to practice and refine the theory learned in class. You do not have to turn in these problems. Homework is going to be assigned after every section we cover in class. It is critical that you complete these assignments - the only way to learn math is by doing math!

Graded homework: Some of the assigned homework will be graded and will contribute 30% to your final course grade. The list of graded homework problems will be announced in class and can also be found online. Please turn in the assigned homework on time, that is by the end of class on the day the homework is due.

Written work: We write to communicate. Please bear this in mind as you complete homework assignments and take exams. Work must be neat and legible to receive consideration. You must explain your work in order to obtain full credit; an assertion is not an answer. For specific suggestions see A guide to writing in mathematics classes.

Disabilities: Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, stop by the Office of Disability Services to register for support services.

Suggestions:

1. Attend class. You are always responsible for what is discussed in class, including announcements and discussions of material that is not covered in the book. If you miss a class, get a copy of someone's notes.
2. Do NOT fall behind. 
3. Try to study with others in small groups. This is a great way to learn.

Lectures and homework assignments:
In the table below the sections in a given chapter are enumerated as §(chapter).(section). For example §2.3 is the third section in chapter 2: "RAA proofs". The notation E3 refers to "Exercise 3" while MA3 refers to "Major exercise 3". The letters RE stand for "Review Exercises".

Date	Topic covered	Read	Homework
August 28	The origins of geometry	Thales, Pythagoras Plato, Euclid §1.1	Math 475 Read §1.7 and §1.8 §1-E: 1-3,8-10,12,13  Math 675 Read §1.7 and §1.8 §1-E: 1-3,8-10,12,13 MA: 1,4,7
	The axiomatic method	§1.2
	Undefined terms	§1.3
August 30	Euclid's first four postulates	§1.4
	The parallel postulate	§1.5
	Attempts to prove the parallel postulate	§1.6
September 6	Informal logic	§2.1	Math 475 §2: RE 1-20 E: 1-5 Math 675 §2: RE 1-20 E: 1-5
	Theorems and proofs	§2.2
	RAA proofs	§2.3
	Negation	§2.4
	Quantifiers	§2.5
	Implication	§2.6
	Law of excluded middle and proof by cases	§2.7
September 11	Incidence geometry	§2.8	Math 475 §2: E 7-12 Math 675 §2: E 7-12 ME 1,3,6,7
	Models	§2.9
September 13	Isomorphisms of models	§2.10
	Projective and affine planes	§2.11
September 18	Flaws in Euclid	Hilbert, Reid §3.1	None.
September 20	Axioms of betweenness	§3.2	Math 475 §3: E 1-19 Math 675 §3: E 1-19
September 25	Axioms of betweenness	§3.2
September 27	Axioms of congruence	§3.3	Math 475 §3: E 20-36 Math 675 §3: E 20-36
October 2	Axioms of congruence	§3.3
October 4	Axioms of congruence	§3.3
October 9	Axioms of continuity Axiom of parallelism	§3.4 §3.5	None.
October 11	Alternate interior angle theorem Exterior angle theorem	§4.2 §4.3	Math 475 §4: E 2-5,9,10,15 17-20,24,27,30 Math 675 Same as Math 475 + §4: ME 3-5
October 16	Measure of angles and segments Saccheri-Legendre theorem	§4.4 §4.5
October 18	Equivalence of parallel postulates Angle sum of a triangle	§4.6 §4.7
Midterm Exam for 475/675 - Due Wednesday, November 1st.
October 23	Hyperbolic geometry	§6.5	Math 475 §6: E 2,4,5,9,11,12,16 Math 675 §6: E 2,4,5,9,11,12,16
	Angle sums (again)	§6.6
	Similar triangles	§6.7
	Parallels with a        common perpendicular	§6.8
October 25	Limiting rays	§6.9
	Consistency of hyperbolic geometry	§7.1	Math 475 §7: E  Math 675 §7: E  NonEuclid
	The Beltrami-Klein model	§7.2
October 30	The Poincare models	§7.3
	Perpendicularity in the Beltrami-Klein model	§7.4
	A model of the hyperbolic plane from physics	§7.5
	Inversion in circles	§7.6
November 1	Inversion in circles	§7.6
November 6	Inversion in circles	§7.6
November 8	Inversion in circles	§7.6
November 13	Inversion in circles	§7.6
November 15	Inversion in circles	§7.6
November 22	Triangles in hyperbolic geometry: Angle sums	Mathematica script	To view, download the free MathReader.
November 27	Triangles in hyperbolic geometry: Angle sums	Mathematica script
November 29	Triangles in hyperbolic geometry: Area of triangles	§10.1
December 4	Hyperbolic trigonometry	§10.5
Final exam for 475/675 - Due by noon on Monday , December 18th.
December 6	Hyperbolic trigonometry	§10.5
December 11	Review for final exam

Graded homework assignments:

Solutions for Graded homework assignments: