5.3+&+5.4+Comments

Mindscapes for Chapter 5.3 & 5.4 please post original response by Friday 11/5(noon) and classmate responses by Sunday 11/7 (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: __** 5.3 Postings: **__

2) [JEH003] I think for this problem the answer is 0, although I'm not 100% sure if I'm supposed to count one or two faces on this shape so if 2 faces is the case then the answer would be 1. Chris: The answer is 2. Each hole is one region, plus the white space all around the shape =] FAB001: The equation looks like... 5-6+3=2

Nice job! [ShariL] 3) [ljj001]

5) [KLK002] : A rectangle ( like a tissue box ) has 8 Vertices  12 Edges  6 Faces and V -E + F = 2

A rectangle is 2-d and a tissue box is 3d? [ShariL]

 MRH003: I got the same answer by finding a rectangular solid at my house and counting. SMD001: I did the same thing with a rectangle at home. It was easier to see it 3D than to think about it in your head.\ Chris: I just did it was a book :) It's right!

7) [jtl001] - Josh where are you????[Shari L]

8) [csv001] Chris: When you take a line and add a dot in the middle to make a new connected graph we get this: 3 Vertices, 2 edges, and 1 region. If we do V-E+F it equals two. This formula (vertices - edges + regions) it will ALWAYS equal two. It is called the Euler Characteristic.

Super job! [Shari L]

9) [fab001] It is not possible to reduce the number of regions by adding an edge to the graph. The number of regions that exist can only be added onto or kept the same by increasing edges. The object can be split in any direction or the edge can trail off into space. V-E+F=2 V-(E+1)+(F-1)=2? This formula does not even out to 2 like the one above it, there is a subtraction of 2, instead of a balancing out. (V+1)-(E+1)+F=2? If we add a vertex it becomes an equivalent formula, so it is possible to add an edge and maintain regions.

SMD001: I got that answer to. You can make more regions but you can't take away any by adding an edge.

[ Or keep the number of regions the same! - Shari L]

Chris: That makes sense. How would you ever be able to take away a region? I don't get it.

11) [trc002] - I am sorry but I could not get this one, I looked throughout chp4 sec6 and I found nothing on it. [ TRC where are you???? Your classmates need you to participate - Shari L]

__** 5.4 Postings: **__

1) [SMD001]:Which of the knots below are mathmatical knots? (see the 4 pics in your book).. Answer:The first knot pictured itsn't really a knot it is just layed over itself; they called this the unknot. The second one is a knot, it is the Trefoil Knot. The third knot isn't a knot it's a unknot again because it is just twisted over itself. The last knot is a math math knot because you can't just untwist that knot it looks like it is a real knot.

2) [nmg 002] ﻿"Any unknotted curve" It is pictured in the book as simply a circle FAB001: The unknot is a circle

3) [mrh003] Crossing Count: Count the crossings in each knot below. The first figure has 3 crossings. The second figure has 0 crossings. The third figure has 5 crossings. FAB001: I came up with the same answers. So I think this is right. SMD001: I got the same numbers. It's a pretty straight forward question. You got it! [Shari L]

4) [ JEH003]Does anyone know how to figure out whether or not the figure in this problem is a knot or a link? If I had to guess I would say it's a link but I'm not 100% sure by any means. FAB001: I think it looks like a knot, I looked through the text but did not find a good definition for both of them in the sections. I could use some help on this as well.

Check out pages 380-381 for examples of links the are "rings" that are interconnected and knots are one string configured into a knot which is discussed on page 377-380 [ShariL].

5) [ ljj001] Borromean ring is three circles that are linked by removing any one ring it results in two unlinked rings.

6) [KLK002] ﻿ Where are you?? We need you to participate!!! ﻿I'm sorry... the activity requires the participation of 4 -5 people. I haven't been with that many people to do the activity.. Im trying to find a group to help me & I can share my results.