Graded Assignment
MTH203B/204B Geometry | Unit 6 | Lesson 16: Beyond Euclidean Geometry Unit Test
Name: Ryan Rosier
Date: 5/22/15
Graded Assignment
Unit Test, Part 2
Answer the questions. When you are finished, submit this test to your teacher by the due date for full credit.
(18 points)
1. The graph below represents five cities and the routes between them. An out-of-state road
inspector is asked to fly into Pottsville (P). From Pottsville, the inspector must inspect each
road on the map, making only one trip along each road, and then fly out of Tinkertown (T).
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a.) Will the road inspector be able to complete the inspection as described? Mathematically explain why
or why not and, if such an inspection is possible, describe the route. Yes, it is mathematically possible
because the degree of vertices for P=3, T=3, M=2, C=4, and R=2 and in Euler’s theorem, the graph
has to be connected, which in this case it is and the number of vertices in the graph whos vertices is
odd, is 0 or 2. And in this case, we have 2 that have a degree of vertices that are odd, therefore
mathematically this is possible for the driver. The route would be P>R>C>M>T>C>P>T.
b.) The inspector would prefer to fly into and out of the same town, but still drive each road only once.
Would that be possible? Mathematically explain why or why not and, if such an inspection is possible,
describe the route.
c.) Below, the map has been expanded to show additional cities and routes. A trucker who lives in
Jonesboro (J) needs to make deliveries in each town and then return home without passing through
any of the towns more than once. What type of mathematical circuit is the trucker hoping to use? If
the trucker can complete the circuit, describe the route. The driver would use a Hamiltonian circuit.
The route would be J>R>A>C>V>M>T>P>J.
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Page 1 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 6 | Lesson 16: Beyond Euclidean Geometry Unit Test
© 2010 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 6 | Lesson 16: Beyond Euclidean Geometry Unit Test
Answer:
(10 points)
2. Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these
points:
Score
a.) Describe the role of the Parallel Postulate in spherical geometry.
b.) How are triangles different in spherical geometry as opposed to Euclidean geometry?
c.) Geodesics
d.) Applications of spherical geometry
Answer:
While in Euclidean geometry the parralel postulate or axim of Euclid gives us, for any given point not on a given
line, one and only one straight line through the point that is parallel to the given point, in spherical geometry,
where great circles count as "straignt lines" relative to the sphere's surface, there are *no* lines through that given
point, parallel to the given "line" (or great circle). (In fact, the two straight "lines" will intersect twice, at two
antipodal points.)
b.) How are triangles different in spherical geometry as opposed to Euclidean geometry? The difference is that in
Euclidean geometry the interior angles of any triangle add up to a straight angle (i.e. 180 degrees, or (pi) radians),
but in spherical geometry, they may add up to quite a variety of quantities. In spherical geometry, the smaller the
triangle, the more closely it approximates a triangle in Euclidean geometry, but the larger it is, the less. Consider
the equator divided into three segments: that would be a spherical triangle with interior angles that add to 3*180
degrees!
c.) Geodesics is the surveying of areas on the surface of the Earth that are large enough for the curvature of the
Earth to matter, and that spherical geometry (and especially spherical trigonometry as well) are useful because
the Earth's shape is, to first approximation,
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Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 6 | Lesson 16: Beyond Euclidean Geometry Unit Test
(7 points)
3. Use your knowledge of computer logic to answer these questions.
a.) 10001 base 2
= ___17___
b.) 1101101 base 2
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base 10
= _109____
base 10
c.) What type of gate does this input-output table correspond to? OR
Input
Output
A
B
?
0
0
1
1
1
0
0
1
1
0
1
1
d.) The expression that describes the network of logic gates:
Is [A AND (NOT B)] OR (NOT B). Complete the input-output table for the network:
Answer:
Your Score
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Copying or distributing without K12’s written consent is prohibited.
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