#$&* course mth 152 12/12 2:00 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. ** STUDENT COMMENT OK, not so sure how they intersect even on a sphere. I see they will connect with themselves, but not how the parallel intersect. INSTRUCTOR RESPONSE If you start here and go due north, while I start 100 miles to the west and go due north, then we are moving in parallel directions. If we both continue moving due north, we will always be moving parallel, and we will meet at the north pole. The Earth isn't quite a perfect sphere, so this isn't literally true, but it would be as described on a perfect sphere. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.7.18 ruler r.b. CD wrench nail **** To which of the objects is the coin topologically equivalent and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Ruler and the Nail. Because they are the only objects with ZERO holes and all the other objects contain at least one hole. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: ********************************************* 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 of 3 or more. because it has three holes punched through one sheet of paper confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The genus of this sheet of paper is 3 becasue it contains 3 holes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.7.42 3,3,3,3,4,4,2,2 **** Can the network be traversed or not and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: NO. it contains more than two ODD vertices. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: ********************************************* 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: Are you're saying to start at a vertex that has three paths meeting at that vertex? Or are you saying a network that has an odd number of vertices (3) and you start at vertix numbered 3? I""m very confused by your wording! If your saying to start at a vertex that has three paths that meet there, you could not end there because you leave on one path, then arrive to the vertex on the second path and leave on the thrid path and have no way to return, but there is nothing here to say if that is the last, or if it is the only, odd vertex. If the network has three vertices, you may not be able to end there because in order to be able to traverse the network, you have to have an even number of ODD vertices and that is not stated. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** You can’t start on a vertex of order 3 and end up on the same one. You leave the vertex along the first of the three edges. When you traverse the second of these edges you are returning to the vertex, and when you leave again you have to travel along the third and you can't get back. You can end up on a different vertex of degree 3 if there is one (and if there is one you must end on it), but you can't end up on the degree-3 vertex you started from. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q **** If you start on a vertex of order 4 can you traverse the network and end up not on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I need to be ale to visualize what it is you are asking. I look at the given answer and do not understand what is being asked. The book says, ""It is acceptable to go through a vertex as many times as needed."" page 605 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: ********************************************* 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: Still confused by the your use of the word ""order"". When I look at the given solution I deduce that you are using ""order"" to mean paths or arcs? Meaning that the vertex in the question is an even vertex? If so then you cannot end on that vertex because on your second trip there, you would get stuck with no way to get out confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 2 and traverse the network you leave on the first edge, return on the 2 nd and you’re stuck there. ** No, because once again this is an even vertex. One point must be the starting point and one the ending point. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q **** If you start off of a certain vertex of order 3 and traverse the network is it possible to end up somewhere besides this vertex? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If your saying to start at a vertex that has three paths that meet there, you could not end there because you leave on one path, then arrive to the vertex on the second path and leave on the thrid path and have no way to return, therefore you would have to end up somewhere else. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. *&$*&$ I feel like I understand the concepts, just not the change in wording of the last questions. When it comes to the exam, should I know what the word ""order"" means in relationship to networks, and if so, could you clarify? " 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. *&$*&$ I feel like I understand the concepts, just not the change in wording of the last questions. When it comes to the exam, should I know what the word ""order"" means in relationship to networks, and if so, could you clarify? "