5.1+&+5.2+Rubbersheet+Geometry

Mindscapes for Chapter 5.1 & 5.2 please post original response by Friday 10/29(noon) and classmate responses by Sunday 10/31 (noon). If you need to post a drawing or handwritten work and do not have the capability to scan it as a .jpeg it must be submitted to my mailbox (Basement of AB building) by noon on Thursday and I will post in on Friday: 5.1 1) [fab001] (jeh003) For this the books describes equivalent by distortion as when two objects can be shrunk, bent, or twisted without cutting or gluing and can be deformed into the other one. 5.1 2) [ trc002] I would say yes it is equivilant. you can flaten the toilet paper tube and shape it to look similar to a CD. mrh003: I agree. This is similar to the example we were given in class on Monday, when she made the cylinder shape and flattened it out to look like a CD. csv001: Yeah. From what we did in class, the toilet paper should be equivalent to the CD. They both have the same amount of holes, and faces, and regions. right? Good things come from attending class! [ShariL] 5.1 3) [SMD001]: Find a large rubber band and stretch it with your fingers to make a triangle, then a square, and then a pentagon. Are these shapes equivalent by distortion? What other equivalent shapes could you make with the rubber band? Can you stretch it to make a rubber disk? **Answer**: I think that they are all equivalent by distortion. I think that you could also make a lot more shapes that were eq. by distortion. With the question about the disk i'm not sure if they are asking if we can make one that is filled in with the rubber band or if it just needs to be a circle?
 * Comment**: you could also make a rectangle

5.1 4) [nmg002] I posted it in the discussion because I just was able to get this page to edit to work. Every time I try to edit I get a blank page. So here it is.
 * || [|uraqtinvu]

5.1 #4

x=4 y=3 z=2 ||

Where are you??? Where is this answer?

5.1 7) [mrh003] Your ABC's (H). Consider the following letters made of 1-dimensional line segments: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z. Which letters are equivalent to one another by distortion? Group equivalent letters together. **Answer:** Letters with one edge and one region: C,E,F,G,H,I,J,K,L,M,N,S,T,U,V,W,X,Y,Z. Letters with two edges and two regions: A,O,P,R. csv001: this is a bizarre question, but I love it! At first I got it confused with vertices and I was wanting to say that W for instance had 4 edges. But then I remembered that it only matters with how many times you can get around the object. So your answer is correct!!! =] The letter B stands on its own with three edges and three regions. This is kind of difficult. I think that a lot of these can be made with the same piece of string. For sure it feels like G, C, S, and U can be eq. by distortion and that is only because the curves are similar and i think can be made with the same string. However S might need a longer string than C. So it gets complicated. So i guess I just really dont know either. lol. ~Uraqtinvu

I do not agree with all of these....can some other people join the discussion please. Think of these made of yarn or string...so for example "C" and "G" could be made with one piece and just shape it differently so they are the same...but "E" you would have to have the one piece to form with the outside "[" part and you would a another little piece for the center part to make the whole "E". Now lets reorganize SOME of these letters....[ShariL]

5.1 16) [JEH003] I don't believe that these cuts in the paper would be equivalent because on each the folds are the same but the cuts are in different spots, which changes the amount of holes on each page.

Are are all the pieces paper different or are some equivalent? [ShariL] 5.1 20) [ljj001]: Starry-eyed. Looking at the two stars I believe that they are equivalent by distortion they have the same number of edges, surfaces, and spaces.

SMD001: I think so to because they have the same number if they didn't it wouldn't work.

Klk002: true, if they didnt have the same amount of edges, surfaces and spaces, it wouldn't work.. so I think they do too.

csv001: I agree as well. although I'm slightly confused.

OK - I will agree too:) [ShariL]

5.2 1) [klk002]: Möbius band is a strip of paper that is connected by tape at the ends of both sides. Before taping the ends together, twist the loop, so you have a band with a half twist in it, making a Möbius band ! csv001: Pretty much :P

5.2 2) [jtl001]How can you look at a loop of paper and determine if it's a Mobius band? The loop of paper is a mobius band if it has a twist in it. And if you draw on the band of paper it should draw the line on the inside and outside. csv001: and it should only have one continuous edge.

Not a "twist" but a "half twist". [ShariL}

5.2 3) [csv001] This is Chris When I made the Mobius Band, with one side being white, the other being blue, the colors meet at the tape line. If you travel along the band with your finger, you can observe that you travel the complete length of both sides of the band. You'll cover every single inch of the paper both white and blue! LJJ001:That's what happened to me too! I kinda like this part. SMD001: I did this to. It's nice to see and do this right before your eyes. mrh003: This made so much more sense when we did it in class. What a great hands on example! klk002: I did that too, but used a pen & saw how you can travel both sides & colors ! So cool !

Thank you for sharing in the excitement! It is more than awesome! [ShariL]

5.2 4) [fab001] ﻿Where is this posting? [ShariL]

5.2 5) [trc002] I believe that she does get a Mobius Band so I would say yes.

Where is this posting? [ShariL]

5.2 6) [SMD001]: For this question I had to have a friend cut a Mobius band and have them guess the outcomes before they cut. Then I had to record what they said. **Reactions**: At first they really didn't understand what I was trying to explain and how it was going to work. Then when I had shown them the process they understood what had happend and why.

LJJ001:Yeah I had my daughter do it and she was hey this is pretty cool I might use it in my geometery class..score one for Mom. Way to go ....moms do know something!

SMD001: Nice! I thought it was helpful to learn.

5.2 8) [nmg002] Once again I posted this in discussion because I was unable to get this page to edit until now.
 * || [|uraqtinvu]

5.2 #8 I am a little stuck here when doing the strip it kind of became a tangled mess. And was even more a tangled mess when I tried to cut it. I tried this twice and had the same result. Uncertain if I did something wrong. Well actually im pretty certain I did something wrong.

When I figure out what is wrong with the wiki edit page ill copy and paste this there.

~uraqtinvu ||

Where is this posting? [ShariL]

5.2 9) [mrh003] Two Twists Again. Take a strip of paper, put two half twists in it, and glue(tape) the ends together. Now cut it lengthwise while hugging the right edge. What do you get? **Answer:** I got the same shape I began with but with a mobius band attached to it. I am not sure if I did it correctly. Is this what everyone else got also? csv001: yes! me too! I had some trouble with the tape falling apart. but I got it eventually and it all worked out =] Yeah its kind of creepy though. It doesn't make sense how they are connected. But hey can't always figure out everything can we? :D ~Uraqtinvu
 * Comment:** Yes, same shape but the 2 bands are connected.