#$&* course MTH 152 4/15 3 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. ** STUDENT COMMENT OK, not so sure how they intersect even on a sphere. I see they will connect with themselves, but not how the parallel intersect. INSTRUCTOR RESPONSE If you start here and go due north, while I start 100 miles to the west and go due north, then we are moving in parallel directions. If we both continue moving due north, we will always be moving parallel, and we will meet at the north pole. The Earth isn't quite a perfect sphere, so this isn't literally true, but it would be as described on a perfect sphere. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I am unsure of this question and the answer that you got, after reading the given answer I am still so what confused.
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Given Solution: The coin is topologically equivalent to the ruler and the nail because none of these have holes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query 9.7.27 genus of 3-hole-punched sheet of paper **** What is the genus of the sheet and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: genus= 3 because of the 3 holes confidence rating #$&*: 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: Cannot be traversed because the network contains 4 odd vertices; in order to be traversed it must only contain 0 or 2 odd vertices. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** This network contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start on a vertex of order 3 can you traverse the network and end up on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: No, because when you travel along that third vertex and don’t return. confidence rating #$&*: 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: No, because once you leave you cannot traverse and not end up on that vertex. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 4 you cannot traverse the network without ending up on that vertex, since you leave the vertex on the first edge, return on the second and leave on the third. If you traverse the network you have to return to the vertex on the fourth edge, and you can’t leave again. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q **** If you start on a vertex of order 2 and traverse the network must you end up on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: No, because you will end up just like the previous two questions; when you have an even number this will always happen. confidence rating #$&*: 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: First off, you travel on one, end up traveling on two, then three. Therefore, you never return. 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: