12/14/11: Final Exam. [Text: Sections 9.3-8, Chapter 10]
12/14/11: Final Exam. [Text: Sections 9.3-8, Chapter 10]
12/14/11: Office hours: 10:30-12:00.
12/13/11: Office hours: 11-12:30 and 3:30-5:10 p.m.
12/12/11: Review via discussion of Sample Exam
III. Solutions of problems which we did
not discuss will be posted on the class web page. [Text: Sections
9.3-8, Chapter 10]
12/7/11: Homework 10 due and discussed. Lines through a given point
perpendicular and parallel to a given line. Area in Poincaré
geometry. [Sections 10.3-4]
12/5/11: Length, angle measure in Poincaré
geometry. Parallelity: ultra and asymptotic. The cross
ratio. [Sections 10.1-3 (through Theorem 7)]
11/30/11: Homework 9 due and discussed. Congruence axioms
(continued). Dedekind's axiom. Parallel axiom. Euclidean geometry is
categorical, but is it consistent? [Sections 9.4-8]
11/28/11: Betweenness and congruence axioms. [Sections 9.3-4 (through
Proposition 12)]
11/23/11: Black Wednesday: this pre-Thanksgiving class, along with my
office hours this week, is canceled and will be made up through extra
office hours before the Final Exam. Happy Thanksgiving!
11/21/11: Discussion of Midterm Exam II. [Text: Sections 7.7-8,
Chapter 4 through Section 4.8, Chapters 5, 6, 8, and 9 through Section
9.2, skipping the 9-team geometry]
11/16/11: Midterm Exam II. [Text: Sections 7.7-8, Chapter 4 through
Section 4.8, Chapters 5, 6, 8, and 9 through Section 9.2, skipping the
9-team geometry]
11/14/11: Review via discussion of Sample Exam II. [Text: Sections
7.7-8, Chapter 4 through Section 4.8, Chapters 5, 6, 8, and 9 through
Section 9.2, skipping the 9-team geometry]
11/9/11: Homework 8 due and discussed. Axiomatic geometry. Incidence
axioms. Other models of geometry. [Text: Introduction to Chapter 9 and
Sections 9.1-2]
11/7/11: Conformal mappings: similarity, inversion in a circle, angles
between curves. [Text: Sections 8.1-3]
11/2/11: Homework 7 due and discussed. Polygons and circles. [Text:
Sections 6.2-3]
10/31/11: Trigonometry. Trigonometry of triangles. Quadrangles. [Text:
Sections 5.1-2 and 6.1]
10/26/11: Homework 6 due and discussed. Triangles: the Euler line,
angle bisectors and incenter. [Text: Section 4.8]
10/24/11: Triangles: orthocenter, area, Heron's formula,
circumcenter. [Text: Sections 4.5-7]
10/19/11: Homework 5 due and discussed. A few words on classification
theorems for isometries. Symmetries of figures. Triangles: angle sum,
centroid. [Text: Sections 7.7-8 and 4.1-4]
10/17/11: Midterm I discussed. [Text: Chapters 1, 2, skipping Sections
2.1 - 2.2, Chapter 3, Sections 7.1-5]
10/12/11: Midterm Exam I. [Text: Chapters 1, 2, skipping Sections 2.1
- 2.2, Chapter 3, Sections 7.1-5]
10/5/11: Homework discussion. Isometries: reflections, central
inversion, rotations. [Text: Sections 7.3-5]
10/3/11: Homework problem 3.8.24. Isometries: identity,
translations. [Text: Sections 7.1-2]
9/28/11: Homework due at the beginning of class. Homework
discussion. Congruence of triangles. Life in barycentric
coordinates. Changes of coordinates. [Text: Sections 3.5-7]
9/26/11: Barycentric coordinates. Linear transformations and
isometries. Congruence. [Text: Sections 3.2-4]
9/19/11: Angles and angular measure. Arccos. [Text: Sections 2.1
(through Definition 3), 2.3-4]
9/14/11: Homework due at the beginning of class. Homework discussion
(Problems 1.7.21, 26, and 28). Lengths for line segments (the triangle
inequality, Pythagorean theorem). Distance from a point to a
line. [Text: Sections 1.5-6]
9/12/11: Subsets of lines: segments and rays. The concept of
betweenness. Lengths for line segments (through
Cauchy-Schwarz). [Text: Sections 1.3-5 through Lemma 29]
9/7/11: Introduction. Points, lines, and incidence. Parametric
equations of lines. Some Linear Algebra. A proof of Euclid's
axiom. (It is rather a proof of the fact that in our model of
geometry, Euclid's axiom is true.) Orthogonal vectors. Normal
equations of
lines. [Syllabus. Review
Linear Systems of
Equations. Section
1 of Description of 5335 by Prof. Roberts. Text: Chapter 1 through
Section 1.2. Section 1.4 through Lemma 23]