#$&* course Mth 152 Nov 29 - 11:39pm Question: `q Query 9.7.6 - intersecting lines m, n parallel to k **** In which geometry or geometries is this possible and why?
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Given Solution: ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. ** STUDENT COMMENT OK, not so sure how they intersect even on a sphere. I see they will connect with themselves, but not how the parallel intersect. INSTRUCTOR RESPONSE If you start here and go due north, while I start 100 miles to the west and go due north, then we are moving in parallel directions. If we both continue moving due north, we will always be moving parallel, and we will meet at the north pole. The Earth isn't quite a perfect sphere, so this isn't literally true, but it would be as described on a perfect sphere. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): okay ------------------------------------------------ Self-critique Rating: okay ********************************************* Question: `q Query 9.7.18 ruler r.b. CD wrench nail **** To which of the objects is the coin topologically equivalent and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: It’s equivalent to the nail. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): Even if it doesn’t have a hole, why the ruler? ------------------------------------------------ Self-critique Rating: 1
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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): okay ------------------------------------------------ Self-critique Rating: okay ********************************************* 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: It’s odd and cannot be traverse because it has an odd number of vertices. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** This network contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): okay ------------------------------------------------ Self-critique Rating: okay ********************************************* Question: `q **** If you start on a vertex of order 3 can you traverse the network and end up on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I don’t understand this at all. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): I don’t understand this at all. ------------------------------------------------ Self-critique Rating: 1
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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): okay ------------------------------------------------ Self-critique Rating: okay ********************************************* 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: If you go out on the 1st, and return on the second you will end up back on the vertex. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 2 and traverse the network you leave on the first edge, return on the 2 nd and you’re stuck there. ** No, because once again this is an even vertex. One point must be the starting point and one the ending point. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Why does it not? I thought if it went out 1st and returned on the second it would be back on the line. ------------------------------------------------ Self-critique Rating: 2 ********************************************* Question: `q **** If you start off of a certain vertex of order 3 and traverse the network is it possible to end up somewhere besides this vertex? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If you go out on the 1st, return on the 2nd, go back out on the 3rd, you do not end up back on the line. confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): okay ------------------------------------------------ Self-critique Rating: okay