| Date |
Topic |
Reading Assignment |
Homework Problems |
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| Thursday, Aug. 30 |
Course Procedures and Policies
Playing with models |
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Tuesday, Sept. 4
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A Brief Historical Perspective: Euclid and his Elements. |
Chapter 1 of Venema
Group reading assignment
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Short Powerpoint presentation on group reading assignment. A prepared presentation of some matheamtics from the group reading assignment. |
| Thursday, Sept. 6 |
Incidence Geometry |
Chapter 2 of Venema (You may skim 2.1 and 2.5.) |
Class problems: Exercises 1, 3, 4, 5, 8 and your choice of 2 or 6 at the end of Section 2.6. |
|
| Tuesday, Sept. 11 |
Existence and Incidence Axioms
Distance and the Ruler Postulate |
Sections 3.1 and 3.2. |
Class problems: Exercises Section 3.2; 17, 18, 19 and problem assigned individually.
Notebook problems: Section 3.2; 1, 5, 7, 12. (Think about what #12 is talking about!) |
| Thursday, Sept. 13 |
Plane Separation |
Section 3.3 |
Class Problems: Exercises 3.3; 3 and 5. Proofs of Thms 3.3.9, 3.3.10, and 3.3.12.
Notebook Problem: Section 3.3; 1, 2.
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| Tuesday. Sept. 18 |
Introduction to Geometer's Sketchpad
Finish with Plane Separation
Begin work on the Protractor Postulate |
Section 3.4 |
Presentation of book proofs, as assigned. (See detailed assignments and instructions in the email!)
Class Problem: Exercises 3.4; 1 |
| Thursday, Sept. 20 |
Finish with the Protractor Postulate
Crossbar and the Linear Pair Theorem
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Section 3.5 through the Vertical Angles Theorem (3.5.13) |
Presentation of book proofs, as assigned.
Notebook Problems from 3.2 and 3.3 due. |
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| Tuesday, Sept. 25 |
Crossbar and the Linear Pair Theorem, (cont.)
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Section 3.5 through Theorem 3.5.13 ---AGAIN!!! |
Class Problems: Exercises 3.5: 2, 3, 5
Notebook Problems: Exercises 3.5: 1, 4, 6. |
| Thursday, Sept. 27 |
Finish any remaining parts of 3.5
The Side-Angle-Side Postulate
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Sections 3.6 and 3.7 |
Come with Questions from the readings (and on notebook problems!) |
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|
| Tuesday, Oct. 2 |
Exterior Angle Theorem
Triangle Congruence |
Sections 4.1 and 4.2 |
Notebook Problems from 3.5 due.
Class Problems:Exercises 4.2; 1, 2, 5 (existence).
Notebook Problems: Exercise 4.1; 1. Exercises 4.2; 4, 5 (uniqueness!).
|
| Thursday, Oct. 4 |
Three Inequalities for Triangles |
Section 4.3; pgs 77-79 |
Class Problems: Exercises 4.3; 1, 6, 7
Notebook Problems: Exercises 4.3; 2, 3, 4. |
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|
| Tuesday, Oct. 9 |
Quiz # 1---Proofs of Thms 4.1.2 & 4.1.3.
Angle and Perpendicular Bisectors |
Rest of Section 4.3 |
Class Problems: Exercises 4.3; 8, 9. |
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| Thursday, Oct. 11 |
No Class---October Reading Days
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| Tuesday, Oct. 16 |
Alternate interior angles; existence of parallels |
Section 4.4 |
Class problems: Exercises 4.4; 1, 2, 3. Carefully read through the Alternate Interior Angles Proof and corollary on existence of parallels.
Notebook Problems from 4.1, 4.2, and 4.3 due. |
| Thursday, Oct. 18 |
Sneaking up on non-Euclidean geometry:
Saccheri-Legendre Theorem.
Takehome Midterm Distributed
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Section 4.5 |
Class problems: Exercises 4.5; 1, 2. |
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| Tuesday, Oct. 23 |
In-Class Midterm
(Takehome Midterm Due at the beginning of the hour) |
| Thursday, Oct. 25 |
Introducing quadrilaterals |
Section 4.6 |
Class problems: Exercises 4.6; 1, 2, and 5.
Notebook Problems: Exercises 4.6; 4, 7, & 10. |
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|
| Tuesday, Oct. 30 |
Equivalences to the Parallel Postulate |
Section 4.7 |
Class Problems: Exercises 4.7; 1, 2, 6 and "expert" presentations.
Notebook Problems: Exercises 4.7; 3, 4, 5. |
| Thursday, Nov. 1 |
Same as the assignment for Tuesday |
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| Tuesday, Nov. 6 |
(Crazy) Class Project, as implicitly promised. |
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Notebook Problems from 4.6 and 4.7 due. |
| Thursday, Nov. 8 |
Rectangles and Defect. |
Section 4.8 (read through page 101 carefully for content. Work on Lambert and Saccheri Quads.) |
Class problems: Exercises 4.8; 5, 8. Notebook problems: Exercises 4.8; 6. 7, 9, 10. |
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| Tuesday, Nov. 13 |
Basic theorems of Euclidean geometry and the Parallel Projection Theorem. |
Sections 5.1 and 5.2 |
Class problem: Exercises 5.1; 2
Notebook Problems: Exercises 5.1; 3, 6, 7, 8 and 5.3; 2.
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| Thursday, Nov. 15 |
Exploring the Euclidean Geometry of the Triangle (w/ Geometer's Sketchpad) |
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Work in class on exploratory exercises. |
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| Tuesday, Nov. 27 |
Class Presentations on Triangle Exploration. |
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Class Problems from Exploratory exercises. |
| Thursday, Nov. 29 |
Basic Theorems of Hyperbolic Geometry. Introducing Parallels. |
Sections 6.1 and 6.2 |
Class Problems: Section 6.1; 2,3; Section 6.2; 1.
Notebook Problems: Section 6.1; 1, 6ab. Section 6.2; 2, 3.
Notebook Problems from 4.8, 5.1, 5.3 and Median Concurrence Theorem due. |
|
| Tuesday, Dec. 4 |
The Angle of Parallelism
Introducing Asymptotic Parallel Rays |
Section 6.3 and Section 6.4 through the bottom of page 146. |
Notebook Problem: Section 6.4; 1 |
| Thursday, Dec. 6 |
Existence of Asymptotic Parallel Rays
Discussion of Asymptotic Triangles |
Read Rest of Section 6.4 and Section 6.5 |
Presentation of book proofs, as assigned. (See detailed assignments and instructions in the email!) |
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| Tuesday, Dec. 11 |
Classifying Parallels |
Section 6.6 |
Presentation of books proofs, as assigned.
Class Problem: Section 6.6; 1.
Notebook Problem: Section 6.6; 2. |
| Thursday, Dec, 13 |
Properties of the Critical Function and Basic Facts about Triangle Defect
Takehome Final Distributed! |
Section 6.7 and Section 6.8 through the bottom of Page 162. |
More presentation of book proofs, as assigned.
Class Problems: Section 6.7; 1, 4.
Notebook Problems from 6.1, 6.2, 6.4 and 6.6 due. |
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Final Examination
In-Class Exam---Tuesday, December 18, 2011 from 9:30 to 11:30 a.m
Takehome exam---due by 5 p.m on Tuesday, December 18.
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