course Mth 152 ĐhӵԨCassignment #025
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13:21:03 **** 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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RESPONSE --> Lobachevskian
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13:21:08 ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. **
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RESPONSE --> ok
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13:22:16 **** query 9.7.18 ruler r.b. CD wrench nail **** To which of the objects is the coin topologically equivalent and why?
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RESPONSE --> A, E Because both have zero holes, or circles.
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13:22:27 The coin is topologically equivalent to the ruler and the wrench nail because none of these have holes.
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RESPONSE --> ok
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13:23:21 **** query 9.7.27 genus of 3-hole-punched sheet of paper **** What is the genus of the sheet and why?
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RESPONSE --> 3, Because it has three holes on its surface.
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13:23:24 The genus of this sheet of paper is 3 becasue it contains 3 holes.
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RESPONSE --> ok
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13:25:37 **** query 9.7.42 3,3,3,3,4,4,2,2 **** Can the network be traversed or not and why?
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RESPONSE --> Traversible, because there are two corners that have an odd number of networks.
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13:25:50 ** This network contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot. **
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RESPONSE --> ok
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13:26:15 **** 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.
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RESPONSE --> ?
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13:26:36 ** You cant 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. **
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RESPONSE --> ok
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13:27:46 **** 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.
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RESPONSE --> Yes, because the first can be the one where it goes away from the vertex, then it comes back, goes away again and comes back at the end to make 4.
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13:28:04 ** 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 cant leave again. **
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RESPONSE --> ok
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13:29:08 **** 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.
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RESPONSE --> Yes, because you use one vertex to leave it originally and you cannot leave the vertex once you come back to it again.
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13:29:14 ** 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 youre stuck there. **
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RESPONSE --> ok
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13:29:21 No, because once again this is an even vertex. One point must be the starting point and one the ending point.
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RESPONSE --> ok
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13:29:34 **** 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?
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RESPONSE --> Yes
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13:29:48 ** 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 cant travel any of these edges again so you can never return. Therefore you must end up elsewhere. **
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RESPONSE --> ok
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13:29:54 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> Alright"