Math 4900 (4020) - Spring 2007

Review for Exam 3 (May 2, 2007 at 10:30?)

 

Assignment #7: Read 9.1, 9.2 and 9.3.

 

Chapter 9 - Topology

 

Topology is often described as the study of properties of curves and surfaces that are maintained as the curves or surfaces are stretched or distorted. Topological transformations may distort the shape, but leave their "basic structure" intact. See figures 9.5, 9.8, 9.9, 9.10, 9.11 and 9.12. For example, no new endpoints or openings can be created in the transformation.

 

Do Investigation 9.2 on page 268.

 

A network is a collection of points, called vertices, together with a collection of curves called edges, that join the vertices. A traversable network can be traced so that each edge is traced exactly once. If the beginning point and ending points of this tracing coincide, the network is called traversable type 1, otherwise it is called traversable type 2. A vertex is called an even/odd vertex if it has and even/odd number of edges attached to it.

 

Do Investigation 9.3 on page 270. Determine whether the conjectures at the bottom of page 269 are true or false.

 

Homework Due April 25, 2007: Sect. 9.1, 9.2 and 9.3. Mobius Band Handout and Activity 20 (Rubber Sheet Geometry).

Assignment #6: Read 5.1, 5.2 and 7.4. Note that the net for the octahedron on p. 126 is incorrect, since it uses 9 triangles. Visit the following interactive web sites and do the activities: I took a trip on a train. Plot Plans and Silhouettes.

 

Homework Due April 18, 2007: Sect. 5.1, 5.2, 7.4, Cooperative Learning Activity 25, Isometric Explorations, Cross Sections of 3-D Shapes and Transformation Handouts.

 

Review for Exam 2 (Monday, April 9 or 11, 2007)

 

Assignment #6: Read 4.1 (Do investigation 4.1 p. 90) , 4.2 (stop at page 106 optional section) (Do investigation 4.2. p. 103) and 4.3.

 

Homework Due April 4, 2007: Sect. 4.1, 4.2, and three tessellations: one translate, one rotate, and one curved figure. Pick up handouts for these as well as some handouts that will help with the homework as described below. For each tesselation, trace copies to fill an 8.5 inch x 11 inch page.

Pages 30 and 31 go with investigation 4.1, p. 90. I have copies of the shapes for you to borrow if you want.

Page 32, Tesselations of Triangles and Quadrilaterals goes with 4.1 problem #1.

Page 33, Tesselations of Pentominoes goes with 4.1 problem #3.

Page 55, Tesselations of Curved Figures

Worksheet 7-7-1, Making Larger Similar Figures goes with 4.1, problem #5.

I have copies of the shapes for Investigation 4.2, p. 103 for you do borrow if you want.

 

Assignment #5: Read Sect. 3.2 beginning on page 65. You can skip pages 70 and 71, but do the Logo program at the bottom of page 70. Notice that you can use variables in Logo. Just type a colon before the letter. To run the Polygon program, just type POLYGON followed by the value of :N and then the value of :L. Make sure you space between each. Read Sect 3.3 and do the Logo program at the bottom of page 76. Do the Cooperative Learning Activity 10 and then read Section 3.4. It would be a good idea to create figure 3.40 using Sketchpad. Do the medians, altitudes and circumcenters in different colors to help see what is happening.

 

Note the new homework deadline below! Changed again!

 

Homework Due Mar. 19, 2007: Sect. 3.2, 3.3, 3.4 (Do all these using Sketchpad) and Activity 10 handout for Star Polygons (Come by to pick up this handout).

 

Assignment #4: Go through this Sketchpad Tutorial I found on the web. Once you have completed this tutorial, go through parts A, B and C for practice. You can use the software in the lab, buy the student version (click buy now and scroll down to student version, $39.95) or download the free examination copy (you can not save or print in this version, but you can practice and also do screen captures).

 

Homework Due Feb. 23, 2007: The Triangle Exploration here and Computer Exploration 4 on page 395. You can either email you sketchpad file to me, or bring in a printed copy. In the sketchpad file, you can add text boxes to include your name, etc... Make sure that you sketches are dynamic. In other words, only create one parallelogram in exploration 4 and wiggle it a bit to create a new different parrallogram without beginning again from scratch.

 

Review for Exam 1 (February 28, 2007) - I just picked this, so let me know what day is best.) You should be ready for everything except the Sketchpad part. I will post a Sketchpad tutorial and exercises for next week in the next day or two.

 

Assignment #3: Read Sections 2.4, 2.5, & 3.1. Note: There is an error on page 49. A trapezoid has AT LEAST one pair of opposite side parallel. Here is a definition list of quadrilaterals - Quadrilateral Definitions.

 

Homework Due Feb. 16, 2007: Homework Problems: Sect. 2.4, 2.5 (Delete #8) & 3.1 and the Checkerboard challenges. Notice that there are different sized squares! Pentominoes are defined in problem #7 of section 3.1.

 

Click here to view Problem 9 from Section 2.3 with an additional question. You can click on point P and move it around. This was created in Geometer's Sketchpad software that we will learn next.

 

Assignment #2: Read Sections 2.1, 2.2, and 2.3.

 

Homework Due Feb. 5, 2007: Homework Problems: Sect. 2.1, 2.2 & 2.3, Logo 2 handout, and Compass/Ruler constructions handout.

 

I updated the syllabus to show the correct number of 10 pts. per homework.

 

Assignment #1: Read the preface, pages v to ix. Read over the attached Powerpoint Slides about the Van Hiele Levels. Read Chapter One.

 

Download the free Logo software for your computer. It is also available in the third floor computer lab.

Logo software

PC users: Click on the Edall button at the bottom right corner of the screen to bring up the editor. Type in the logo commands in this window. Choose file, save and quit to have those commands activate in the drawing window.

 

Homework Due Jan. 29, 2007: Homework Problems: Sect. 1.1, 1.2 & 1.3 and Logo 1 handout.

 

We will also use Geometer's Sketchpad software that is available in the Claxton labs. Or you can buy the student version or download a free trial version for teachers. The problem with the trial version is that you cannot save files, but it will help you to practice for the exams. Some students have even used the trial version and captured "screen shots" to put in a Word document to print out.

 

60 Day Free Trial of Sketchpad

 

Geometer's Sketchpad software (Click buy now and scroll down to student version, $39.95)