#$&* course Mth 152 12/16/2012 3:16PM 025. ``q Query 25
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Given Solution: ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. ** STUDENT COMMENT OK, not so sure how they intersect even on a sphere. I see they will connect with themselves, but not how the parallel intersect. INSTRUCTOR RESPONSE If you start here and go due north, while I start 100 miles to the west and go due north, then we are moving in parallel directions. If we both continue moving due north, we will always be moving parallel, and we will meet at the north pole. The Earth isn't quite a perfect sphere, so this isn't literally true, but it would be as described on a perfect sphere. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.7.18 ruler r.b. CD wrench nail **** To which of the objects is the coin topologically equivalent and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The coin is topologically equivalent to the nail and the ruler because all of the objects don't have holes in them. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: The coin is topologically equivalent to the ruler and the nail because none of these have holes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.7.27 genus of 3-hole-punched sheet of paper **** What is the genus of the sheet and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It would be genus 3 because it has 3 holes in it. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The genus of this sheet of paper is 3 becasue it contains 3 holes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.7.42 3,3,3,3,4,4,2,2 **** Can the network be traversed or not and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This network can not be traversed because it has more than two odd vertices. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** This network contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start on a vertex of order 3 can you traverse the network and end up on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This is not possible because first you will leave the vertex, then you come back, and finally your only choice is to leave it, so you will not end up on the same vertex you started on. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** You can’t start on a vertex of order 3 and end up on the same one. You leave the vertex along the first of the three edges. When you traverse the second of these edges you are returning to the vertex, and when you leave again you have to travel along the third and you can't get back. You can end up on a different vertex of degree 3 if there is one (and if there is one you must end on it), but you can't end up on the degree-3 vertex you started from. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start on a vertex of order 4 can you traverse the network and end up not on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: This is not possible because first you will leave the vertex, then come back, then leave again, and finally your only option is to come back to the vertex. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 4 you cannot traverse the network without ending up on that vertex, since you leave the vertex on the first edge, return on the second and leave on the third. If you traverse the network you have to return to the vertex on the fourth edge, and you can’t leave again. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start on a vertex of order 2 and traverse the network must you end up on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Yes because first you leave then you have to finish by coming back to that vertex. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 2 and traverse the network you leave on the first edge, return on the 2 nd and you’re stuck there. ** No, because once again this is an even vertex. One point must be the starting point and one the ending point. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start off of a certain vertex of order 3 and traverse the network is it possible to end up somewhere besides this vertex? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: You can only end up on another vertex because it is impossible to start off with a vertex of order 3 and end on the same vertex. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 3 and traverse the network you leave on the first, return on the second and leave on the third edge. You can’t travel any of these edges again so you can never return. Therefore you must end up elsewhere. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. *&$*&$ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. *&$*&$ " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!