Symmetry: The Art of Mathematics Hillyard/Rasmussen
Assignment
6
Due
1) Reading
assignment:
Weyl: pages 41-67
Washburn and Crowe: page 43 to the middle of page 50
2) Draw a
pattern which has a translation.
3) In class
we showed that the group of rigid motions of an equilateral triangle was 
consisting of 6 rigid
motions. Add a design to the equilateral
triangle so that the group of rigid motions becomes 
consisting of 3
rotational rigid motions. Be sure to
justify your answer.
4) Consider
a square (please see the figure below).
a) Find all the reflections and
rotations of the square that send the square
back into itself.
b) Construct the group table for the
square using your reflections and rotations in part a)
c) Can you color the square with two
colors so that the group of rigid motions becomes 
? (consisting of 4 rigid motions) Fully explain your answer.
d) Can you color the square with two
colors so that the group of rigid motions becomes 
? (consisting of 4 rotations). Be sure to justify your answer.