calculus and analytic geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry...

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Clicker Question 1. In a wraparound universe, we can head off straight to eventually come back around. Which are wraparound? a) spherical geometry b) Euclidean geometry c) a Klein bottle d) all of the above e) exactly two of a), b), c) Dr. Sarah Math 1120: Calculus and Analytic Geometry II

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Page 1: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question1. In a wraparound universe, we can head off straight toeventually come back around. Which are wraparound?a) spherical geometryb) Euclidean geometryc) a Klein bottled) all of the abovee) exactly two of a), b), c)

Klein bottle tic-tac-toe: Where should o go next on the main board?

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 2: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question1. In a wraparound universe, we can head off straight toeventually come back around. Which are wraparound?a) spherical geometryb) Euclidean geometryc) a Klein bottled) all of the abovee) exactly two of a), b), c)

Klein bottle tic-tac-toe: Where should o go next on the main board?

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 3: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Klein bottle tic-tac-toe: Where should o go next on the main board?

bottom middle to block x

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 4: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Klein bottle tic-tac-toe: Where should o go next on the main board?

bottom middle to block x

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 5: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Klein bottle tic-tac-toe: Where should o go next on the main board?

also bottom left to block x, so o has no chance of winningDr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 6: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Klein bottle tic-tac-toe: Where should o go next?

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 7: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Klein bottle tic-tac-toe: Where should o go next?

o has no chance of winning

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 8: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question2. What are real-life applications of hyperbolic geometry?a) modeling the internet to reduce the load on routersb) modeling the folds of the brain and Mercury’s orbitc) building crystal structures to store more hydrogen or absorb

more toxic metalsd) more than one of the abovee) none of the above

Latvian/US mathematician Daina Taimina CrochetingAdventures with Hyperbolic Planes

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 9: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question3. How many dimensions does lineland have in Flatland theMovie?

a) one and I have a good reason whyb) one but I am unsure of whyc) two but I am unsure of whyd) two and I have a good reason whye) other

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 10: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question4. Which of the following could Arthur Square see at somepoint in time if a donut is dunked with the hole facing him?Hint: What are cross sections? What would Arthur square see?

a)

b)c) bothd) neither

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 11: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question4. Which of the following could Arthur Square see at somepoint in time if a donut is dunked with the hole facing him?Hint: What are cross sections? What would Arthur square see?

a)

b)c) bothd) neither

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

Page 12: Calculus and Analytic Geometry 2sjg/class/1010/wc/geom/clicker2duniv.pdfa)spherical geometry b)Euclidean geometry c)a Klein bottle d)all of the above e)exactly two of a), b), c) Klein

Clicker Question5. Which of the following arose to demonstrate thePythagorean theorem based on the picture in the Zhou Bi SuanJing or Chou Pei Suan Ching?

a) large square has area c2

b) large square also has area (a − b)2 + 4(ab2 )

c) bothd) neither

Dr. Sarah Math 1120: Calculus and Analytic Geometry II

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