Difference between revisions of "Instructor:Rosette Exercises Solutions"

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(addition to 10.g answer)
(Added answers to # 1 and 2)
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<ol>
 
<ol>
<li>Castrovalva</li>
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<li>Castrovalva: We’re not looking for symmetry as much here as we are looking for some hint of a repetitive pattern. There are many possibilities. Here are but a few.
<li>Reflected F</li>
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* The clouds
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* The windows in the houses on the cliff
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* The leaves on the plants in the fore ground
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* The houses on the bottom right
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* The landscape (plots of land on the right)
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* The patterns in the side of the cliff
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* The trees on the bottom right
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(This is not a very mathematical question. The purpose is to have students look critically at MCE’s work.)
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</li>
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<li>[[Image:Isometries-of-F.jpg]]</li>
 
<li>Rotated F</li>
 
<li>Rotated F</li>
 
<li>A regular polygon with n sides has n reflection lines that meet at the center.  If n is even, there are lines that go from each corner to
 
<li>A regular polygon with n sides has n reflection lines that meet at the center.  If n is even, there are lines that go from each corner to

Revision as of 08:44, 27 September 2007


Rosette Exercises

  1. Castrovalva: We’re not looking for symmetry as much here as we are looking for some hint of a repetitive pattern. There are many possibilities. Here are but a few.
    • The clouds
    • The windows in the houses on the cliff
    • The leaves on the plants in the fore ground
    • The houses on the bottom right
    • The landscape (plots of land on the right)
    • The patterns in the side of the cliff
    • The trees on the bottom right
    (This is not a very mathematical question. The purpose is to have students look critically at MCE’s work.)
  2. Isometries-of-F.jpg
  3. Rotated F
  4. A regular polygon with n sides has n reflection lines that meet at the center. If n is even, there are lines that go from each corner to its opposite corner, and each side to its opposite side. If n is odd, all lines go from a corner through the midpoint of the opposite side.
    1. C4
    2. C3 or C6 if you ignore the black border diamonds - note the crossed arms destroy any mirror symmetry.
    3. None. Details of arms destroy the mirror symmetry.
    4. None.
    5. C5.
    6. C6.
  5. Dali
  6. C1 C2 D1 D2 Not discrete
    FGJLPR NSZ ABCDEKMQTUVWY HIX O
  7. a. D3; b. D1; c. None; d. D1; e. C3; f. D5
  8. C2 symmetry is strongly suggested. A 180° rotation interchanges the devil and Jesus. Also, horizontal and vertical reflections change the figures with the goats. Jesus was a scapegoat - a symbol of blame for the problems of his society. Escher suggests the Devil was instrumental in his scapegoating.
    1. C4. Overlaps prevent D4. The center portion has C8 or even C16 depending on how much you ignore.
    2. C4. Preserving colors reduces to C2.
    3. D3.
    4. C2 is strongly suggested, though not precisely present.
    5. C3 is strongly suggested.
    6. C2 symmetry interchanging colors. No color preserving symmetry.
    7. There is a suggestion of a color interchanging D1 symmetry. But the two sides are not quite the same. (There are also points which are almost centers of C2 symmetry, if only the birds are considered.)
  9. Draw C2-C6, D2-D6 with a motif.
  10. Two rotation centers
  11. This poem can be read normally, or by reading each column of words downwards.