The three types of homework assignments are reviewed below. The date given is the date the assignment is due.

5/27 Study: 5.3/ 2, 3 Turn-in: 5.3/ 5

Journal Explain why it takes two groups of isometries to identify the symmetries of a pattern when color is taken into account.

5/25 Study: 5.2/ 1; 5.3/ 1

Journal Write a paragraph explaining the value of "custom tools" in Sketchpad. Explain what these are and give several examples of situations where they might be useful.

5/20 Study: 5.1/ 1, 4 Turn-in: 5.1/ 2, 3, 7

Toward Your Notebook: Problems 5.1/ 5

Journal An infinite row of Ns has certain symmetries: translational symmetry, rotational symmetry about the centers of the Ns, and rotational symmetry about the midpoint of the segment between adjacents centers of Ns. Is it possible to have a pattern with ONLY the first two types? Explain.

5/13 Study: 4.6/1 Turn-in: 4.4/2, 3, 7; 4.5/ 2, 3; 4.6/ 2

Toward Your Notebook: Problems 4.5/ 8

Journal How do different transformation groups identify different types of geometry?

5/11 Study: 4.4/ 1ab; 4.5/ 1abc and Practice Problems for Quiz 3

Toward Your Notebook: Problems 4.4/ 11

Journal How do you find the inverse of a 3 by 3 affine matrix? Is it as complicated as finding the inverse of a general 3 by 3 matrix?

5/6 Study: 4.3/ 1 Turn-in: 4.3/ 3ad, 4, 6

Toward Your Notebook: Problems 4.2/ 5 & 6 (as one problem)

Journal Why are 3 by 3 matrices used to keep track of transformations of a 2-dimensional plane? Aren't 3 by 3 matrices used to transform vectors with 3 entries?

4/29 Study: 3.4/ 4 Turn-in: 3.3/ 4, 7, 3.4/ 2, 3.5/ 1, 3

Toward Your Notebook: Problems 3.4/ 7

Journal Explain how the area of a triangle is related the sum of its angles in various geometries.

4/27 Study: 3.3/ 1

Toward Your Notebook: Problems 3.3/ 6, including an explanation of what this tells us about the concept of similarity in Saccheri's world.

Journal Saccheri based a lot of theorems on the hypothesis that the summit angles of what we now call a Saccheri quadrilateral are acute, calling it "The Hypothesis of the Acute Angle." What was he trying to do?

4/22 Study: 2.3/4, 2.5/ 2 Turn-in: 1.5/ 4, 13, 1.6/ 3, 6 , 2.3/ 1, 2, 2.4/ 4, 2.5/ 1, 9 (Note: for 2.4/ 4, it's simplest to use Maple. However, if you do not want to use Maple, the computations can be done by hand.)

Toward Your Notebook: Problems 2.5/ 10

Journal Read Flatland and explain the analogy that it gives us for thinking about the 4th dimension.

4/20 Study: 1.5/ 2, 1.6/ 5

Toward Your Notebook: Problems Prove: In triangle ABC, the angle bisector at B divides the opposite side into pieces proportional to the other sides. Also, 1.6/ 12 and 13 (as one problem).

Journal Use geometry to explain why King Kong would not be strong.

4/15 Study: 1.3/ 3, 1.4/1 Turn-in: 4.1/ 1, 3, 4.2/ 2

Toward Your Notebook: Problems 1.4/ 6

Journal Compare the analytic and synthetic methods in geometry. Explain the role of models in geometry.

4/13 Study: 4.1/ 2, 4.2/ 1

Toward Your Notebook: Problems 4.1/ 4

Journal Take a "symmetry walk" around campus and write about what you see. Take paper into the Mission Church and sketch some of the patterns, identifying their symmetries.

4/8 Study: 3.1/1; 3.2/ 1 Turn-in: 1.2/ 7; 3.1/ 4; 3.2/ 2,3

Toward Your Notebook: Problems 3.1/ 5, 6

Journal Is Euclidean geometry the geometry of the so-called real world? How would we know?

4/6 Study: 2.1/ 3; 2.2/ 3 (please bring your paper from 3b to class!)

Toward Your Notebook: Problems 2.1/ 7, 8

Journal Use your notes to describe the 9-point circle. Explain how you would start to give an analytic proof that these nine points all do lie on a circle.

4/1Study: 1.1/ 1, 3, 6, 7ab; 1.2/1, 3, 6, 15 Turn in: 1.1/ 5, 9, 10, 1.2/ 7, 9

Toward Your Notebook: Problems 1.2/ 4, 12; explain clearly how to construct a regular pentagon.

Journal Without looking at your text, describe Euclid’s elements. How would you describe what was unique about Euclid’s achievement?

Stay tuned for future assignments!

Study problems are assigned as exercises to help you digest the material. These will not be collected or graded, but you will have a chance to present your solutions in class (working toward a high score in participation). It would be reasonable for a study problem to have a reincarnation as an exam question. Turn-in problems are just that: Turn them in at the beginning of class (Thursdays only), folded vertically with your name on the outside. Please staple multiple sheets. Our grader will evaluate your work for correctness and effort.

Notebook problems merit careful written solutions, about a page in length. In order to end up with five satisfying solutions for your notebook, you should attempt all the notebook problems assigned.

Journal entries: A journal is a way to keep track of your own ideas, to gain perspective on them by reading them after some time has passed. When a journal entry is assigned, spend just ten minutes writing down your thoughts about that topic. What will this do for you? When the time comes to discuss this topic in class, you will have something on paper to remind you of what you think about it; and should this topic come up as an essay on an exam, you will have already written a draft. I may ask to see your journal at any time, but I will not read it formally or assign you a grade based on this work. I ask you to write up two of your journal entries to add to your notebook.