Section+4.4+Tesselations

We are all going to use the wiki to discuss problems assigned. Look below and you will find the problem that you are responsible to post the first answer for based on your Aquinas e-mail address. It is NOT o.k. to just write "I don't get it". Start by typing the problem (click on edit to start) word for word from the book. You Post your answer as if it were a test question ( You would not leave those blank you would take a stab at it!), HOW you got it (list specific page references and show work) and WHY you did that way. The rest of the class will make comment on at least 3 other problems, corrections, and post their thoughts below your original response. POST THE ORIGINAL RESPONSES BY 10/8 AND THE 3 RESPONSES BY I came on to respond but nothing to respond to! Thursday at 9:52pm [SLewis] Section 4.4 1) [ CSV001] Hello Everybody!! It's chris! I was looking at the shapes. THere are five shapes and I have to answer which of them can be used to tile an entire plane. According to what I can guess. THe square, the right triangle, the abstract rectangle, and the abstract wedge thing can all be tiled. I'm pretty sure the star can't be tiled, but I could definitely be wrong! Any input? Yeah the text does mention the triangle being able to be made into more triangle and I assume you can eventually close it. The only thing about the star is the gaps are larger than the the point the vertices make so I have to agree that you are unable to tile them~Uraqtinvu

2)[mrh003] Shifting into symmetry: Shown below are small sections of three patterns in the plane. Each has several rigid symmetries. For each pattern, describe a rigid symmetry corresponding to a shift. For the first pattern, which resembles fish scales, I believe there is a slide shift. For the second pattern there is a rotation shift. For the third pattern there could be both a slide or flip shift.

The second pattern also has a shift symmetry throughout it, doesn't it? FAB

3)[JEH 003]

4) [ nmg002] I am left quite confused here. I have read this text about 5 times through and cannot grasp the meaning of rigid. Its all too wordy. However based on the patterns I do see only the honeycomb seems to be a true rotational. The last one seems almost reflective and the first fish scale looking one I am unsure of. I know you can rotate the honeycomb one several time and find symmetry. I am not sure what they mean by rigid but the honey comb one is the only one that has rotational symmetry so I don't think it matters what rigid means. I think that they wanted to know the angle of rotation for symmetry, it looks like 45 degrees for the honeycomb. FAB

6)[CSV001] Here's Chris again =] I don't have a scanner available to show you all, but here's my best despriction I had a very difficult time creating a t formation out of only 5 triangles. I tried my best. But it has a pointing stem. I don't think that's allowed It does says in the book something about it being impossible to make a T-arrangement with a 5-unit.~Uraqtinvu SMD001:Comment: Yeah I don't think that it can have a pointed stem. I think you would need one more piece to make it a full stem? Chris: If the book says it's impossible, then that's the answer I suppose!

17) [SMD001]: Question: For each tile below, could copies of it be assembled to create a pattern filling the plane? If so indicate how. The pieces that they show are a rectangle, Octagon, Hexagon, and a triangle. I think that if you had to fill the plane equally you would use the triangle and the rectangle because you could fill a plane evenly with no pieces that are sticking off the plane. If you could use a tile pattern you could use any of the shapes if it doesn't matter if there are pieces that are sticking off the plane.

This question seems weird because it doesn't specify, I think you covered all the possibilities here. It seems like there should be something with more calculations to do. FAB