#$&* course mth 152 12/19/1310:58am
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Given Solution: ** Two parallel lines intersect on a sphere (think of lines of longitude). So this occurs in a Riemannian geometry. ** STUDENT COMMENT OK, not so sure how they intersect even on a sphere. I see they will connect with themselves, but not how the parallel intersect. INSTRUCTOR RESPONSE If you start here and go due north, while I start 100 miles to the west and go due north, then we are moving in parallel directions. If we both continue moving due north, we will always be moving parallel, and we will meet at the north pole. The Earth isn't quite a perfect sphere, so this isn't literally true, but it would be as described on a perfect sphere. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.7.18 ruler r.b. CD wrench nail **** To which of the objects is the coin topologically equivalent and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The coin is topologically equivalent to the ruler and the nail neither of these have holes. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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: its 3 because it has 3 holes confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The genus of this sheet of paper is 3 becasue it contains 3 holes. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query 9.7.42 3,3,3,3,4,4,2,2 **** Can the network be traversed or not and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; 4 odd vertices cannot confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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: contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: This network contains 4 odd vertices. A network with 0 or 2 odd vertices can be traversed; a network with 4 odd vertices cannot. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q **** If you start on a vertex of order 4 can you traverse the network and end up not on that vertex? Explain why your answer must be true. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 4 you cannot traverse the network without ending up on that vertex, the second one ends on the third confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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: If you start on a vertex of order 2 and traverse the network you leave on the first edge, return on the 2 nd No, because this is an even vertex. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a ** If you start on a vertex of order 2 and traverse the network you leave on the first edge, return on the 2 nd and you’re stuck there. ** No, because once again this is an even vertex. One point must be the starting point and one the ending point. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q **** If you start off of a certain vertex of order 3 and traverse the network is it possible to end up somewhere besides this vertex? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 3 and traverse the network you leave on the first, return on the second and leave on the third edge you must end up elsewhere confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. *&$*&$ " 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: #*&!