MATH 406 Geometric Structures

Spring 2005 Assignments and Tests

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Assignment #1 - Due on Wednesday, February 2

If you have not already done so, activate your computer account.

Log in on the campus computer system and do the following:
1) Read any incoming e-mail from your instructor you find in your mail box.
2) If you choose to use an e-mail account other than your SU GroupWise account, you may do so.  However, you must arrange to have your e-mail to your campus account forwarded to your preferred account. "Speedy Sheets" with instructions for using GroupWise can be found at http://helpdesk.salisbury.edu/informationCenter/documentation/speedysheets/speedysheets.htm#GroupWise.
3) Access the home page for this course.  (http://faculty.salisbury.edu/~dccathcart/MATH406/Math406Home.html)
4) Follow the appropriate links and read the course syllabus, your "Instructor's Policies," and the "Guidelines for Written Work.".

Read the author's "Preface" on pp. vii-ix in the text.

Read pp. 1-9 in Chapter 1.  Along with reading the text material, explore some of the web sites suggested by our author and use the resource CD to investigate some results of ancient mathematics.

 

Turn in written solutions for the exercises in parentheses.

Section 1.1 Exercises (pp. 9-10): 1, (2), (4), 5a,b,c; (8)

Be sure to present your write-ups inside the expected cover sheet.

The Prescribed Format for Assignment Cover Sheets.

Links to sample student solutions:  Section 1.1- problem 2,  problem 4,  problem 4 again,  problem 8,  problem 8 again

Assignment #2 - Due on Wednesday, February 9

Remember, we only submit written solutions for exercises in parentheses.

Continue learning to use Geometers Sketchpad.  In your practice with Sketchpad, access and use the files on the CD to

investigate Euclid's Fifth Axiom (Figure 1.2.1) and Playfair's Axiom (Figure 1.2.2).

Read Section 1.2 in the text (pp. 11-20).  Pay particular attention to the discussion of "Axiomatic Systems" on pp. 14-19.

Section 1.2 Exercises (pp. 20-21):  (5)  See a sample solution.  See another sample solution.

Read Section 1.3 in the text (pp. 22-28).

Look over Section 1.4 in the text (pp. 30-39). 

Use the Sketchpad file on the CD to explore the misconceptions regarding trisecting an angle. (Figures 1.4.2 and 1.4.3)

Do the following exercises related to "Axiom System #1.":  1-3, 1-4, 1-5, 1-6, 1-7

(Write up your validation or rejection of our conjecture regarding the way the point in common to the medians of a triangle partitions the medians.)  See a sample solution.  See another sample solution.

(Write up a proof of the following:  In Axiom System 2 there are at least four members and at least two committees.) 

See a sample proof of the theorem stated just above. See another sample proof.

Follow the link to the essay on "The Origins of Geometry."  Read the article for understanding.

 

Assignment #3 - Due on Friday, February 18

 

Re-read Section 1.3 in the text.  In particular, study the proofs of Propositions 6, 10, and 16.

We will be working through the handout on Euclidean Geometry (System 4).  Continue working through that material on your own so you may ask relevant questions in class.  Be prepared to present some exercise solutions or proofs of theorems in class.  Compare our axioms for System 4 with other axiom sets for Euclidean Geometry.

 

Continue learning to use Geometers Sketchpad.  In your practice with Sketchpad, work through Section 2.1 in the text using Geometers Sketchpad and also straightedge and compass to perform the constructions.  Also, work through pp. 63-67 of Section 2.2.

 

Section 2.1 Exercises (pp. 61-62):  (2), (6c)

Section 2.2 Exercises (pp. 72-73):  (2a), (2b), (8c)

 

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Assignment #4 - Due on Friday, February 25

 

Chapter 2 Summary Exercises (pp. 83-84):  (4)  Use coordinate geometry and illustrate with Sketchpad.

 

Test #1 - Friday, March 4

 

Link to a study guide for Test #1

Links to sample solutions for items on Test #1:  Page 1 , Page 2 , Page 3 , Page 4

 

Optional Exercise Set #1 - Present by March 18:  Page 1 , Page 2

 

Assignment #5 - Due on Wednesday March 9

 

Follow the link and read Lecture "Notes #4" by Professor Kuntz.  How do Kuntz's versions of Hilbert's

Axioms for Plane Geometry differ from Hemmer's?

Read pp. 87-90 in the textbook.

Read and work through Section 3.1 in the textbook (pp. 91-96).

Section 3.1 Exercises:  (2)

Link to a solution for Section 3.1 Exercises: 1

 

Assignment #6 - Due on Monday March 14

 

Start working through Section 3.2 in the textbook.  (pp. 98-111).

Section 3.1 Exercises:   (4d)

Section 3.2 Exercises:  (1) In exercise 1 just do three of the six cases (a) A & B on the circle,

(b) one of A & B is on the circle and the other is inside the circle, and (c) both A and B are

inside the circle.  In the last case (c), just show one method.  (4)

 

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Assignment #7 - Due on Friday, March 18

 

Finish working through Section 3.2 in the textbook.

Do investigations on pp. 114-115.

Section 3.2 Exercises:  (7), (8)

Link to a solution for Section 3.2 Exercises: 7

 Link to a solution for Section 3.2 Exercises: 8

Consider the investigation "Introduction to Non-Euclid" on pp. 116-117.

The tool titled "Non_Euclid" can be found at http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html

Using Non-Euclid address the tasks 9 & 10 under "Introduction to Non-Euclid" on p. 117.

Follow the link (Hyperbolic Geometry) and work through the the module on hyperbolic geometry. 

Use either GSP or Non-Euclid as your software tool in doing the activities. Hyperbolic Geometry

 

Assignment #8 - Due on Friday, April 1

 

Work through Section 4.1 in the text.

Section 4.1 Exercises:  1, (2c), 3a,c, (4a,b), (8)

Link to solutions for Section 4.1 Exercises: 2c and 4a

Link to a solution for Section 4.1 Exercises: 4b

Link to a solution for Section 4.1 Exercises: 8

Link to another solution for Section 4.1 Exercises: 8

 

Test #2 - Wednesday, April 6

 

Link to a study guide for Test #2

Be sure you have completed the investigations in Assignment #7 as part of your preparation for

Test #2.  Using Non-Euclid address the tasks 9 & 10 under "Introduction to Non-Euclid" on p. 117.

Also, follow the link (Hyperbolic Geometry) and work through the the module on hyperbolic geometry. 

Use either GSP or Non-Euclid as your software tool in doing the activities. Hyperbolic Geometry

 

Assignment #9 - Due on Monday, April 11

 

Section 4.1 Exercises:  9

Work through Section 4.2 in the text.

Section 4.2 Exercises:  1 all parts, (2), 3, (6), 7

Do the "Investigations" on pp. 156-158 in the text.

Start working through Section 4.3 in the text.

Link solutions for the exercises in this assignment.

 

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Assignment #10 - Due on Monday, April 18

 

Section 3.2 Exercises (p. 113):  (6)

Section 4.2 Exercises: (4)

Finish working through Section 4.3.

Section 4.3 Exercises: 1-6 all, (9), (10)

Start working through Section 4.4.

Section 4.4 Exercises: (2), (4), (6)

 

Assignment #11 - Due on Friday, April 22

 

Finish working through Section 4.4.

Section 4.4 Exercises: (10)

Work through Section 4.5.

Section 4.5 Exercises:  4, 5, (6), 7, (8), 9, (10), 13

Link to a solution for Section 4.5 Exercise: 10

More notes on Section 4.5/#10:  Page 1; Page 2; Page 3

 

Assignment #12 - Due on Friday, April 29

 

Work through Section 4.6.

Section 4.6 Exercises: 1, 3, 5, (6), 7, 8, (10)

 

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Test #3 - Wednesday, May 4

 

Link to a Study Guide for Test #3.

You may use a calculator when working Test #3.

Link to take-home Part II of  Test #3.

Links to Some Tips for Solving Part II Test Items:  #1, #2, #3, #3.b., #4a, #4b

 

Final Exam - 10:15-12:15 am on Wednesday, May 18

 

You may use a calculator when working the final examination.

You may bring one 5" x 7" page of notes to the exam session.

In preparing for the final exam, go over the study guides for the previous tests, and revisit the tests also.

Look at Figure 1.1.6 in the text and the associated construction. Explain why the construction does

indeed produce a valid method for producing the square root of (ab). That is, show that the square

of x is ab. Figure 1.4.14 is similar.

Look at exercises 9 and 10 on page 117. Know how hyperbolic geometry and Euclidean geometry

are similar and how they differ.

 

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