Questions and Answers in the Lab 9 Patterns
Pattern 0
This pattern has only translations, no rotation, reflections
or glide reflections.
- Pick
two of the basic triangle tiles that are at some distance apart and tell
what the translation is as a product of TAB and TAD.
- Write
the product in a different order and trace the triangle again. Since translations commute, you should
end up the same place.
Pattern 1
- Look
for halfturns that are products of two line
reflections.
- Look
at translations. The horizontal and
vertical ones are products of 2 parallel line reflections. Is this true for a "diagonal"
translation (not same row or same column?
Why?
- Look
at translations again, as products of half turns. Are diagonals also products of half
turns?
- Look
for glide reflections as triple line reflections.
Pattern 2
Look for half turn centers.
Also the isosceles right triangles.
Why are there no glide reflections?
Pattern 3
Look for translations that are the products of 90 and 270
rotations.
Look for glide reflections that are the products of 90 rotation and line reflection.
One big idea
Isometry is determined by values on 3 non-collinear
points. There can't be two.