Symmetry: The Art of Mathematics Hillyard/Rasmussen
Class
17 Outline
I) Hand back assignment 12 & 14
II) Review of two-dimensional band
ornaments: summary of our last class
A)
generated
lots of new examples using square & hexagonal grids
B)
examples we found added to our table of previous examples:
|
Example |
Grid type Least restrictive |
Rotations |
Reflections |
Glide Reflections |
|||
|
Example
1 |
Rectangle |
R(360)=I |
r(v) |
None |
|||
|
Example
2 |
Rectangle |
R(360)=I |
None |
Yes |
|||
|
Example
3 |
Rectangle |
R(180) R(360)=I |
r(v),
r(h) |
None |
|||
|
Example
4 |
Rectangle |
R(180) R(360)=I |
r(v) |
Yes |
|||
|
Example
5, we do not have an example of this yet example as drawn in class does not
work |
Rectangle |
R(180),
R(360)=I |
None
|
Yes |
|||
|
Example
6 |
Parallelogram (we
used a rectangular grid in class) |
R(180),
R(360)=I |
None |
None |
|||
|
Example
7 |
Parallelogram |
R(360)=I |
None
|
None |
|||
|
Example
8 |
Square |
R(90),R(180),
R(270),R(360)=I |
r(v),
r(h) |
None |
|||
|
Example
9 |
Square |
R(90),R(180),
R(270),R(360)=I |
None |
None |
|||
|
Example
10 |
Square |
R(90),R(180),
R(270),R(360)=I |
r(v),
r(h) |
Yes |
|||
|
Example
11 |
Hexagon |
R(60),R(120),
R(180),R(240), R(300),R(360)=I |
r(v),
r(h) |
|
|||
|
Example
12 |
Hexagon |
R(60),R(120),
R(180),R(240), R(300),R(360)=I |
None |
|
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III) Go over Assignment 15
A)
Teams:
choose one person to share their example in 1(a) on white board
1)
team
answer to 1(b)
2)
team
answer to 1(c)
B)
Teams:
choose one person to share example for problem 2 on white board
C) Teams: choose one person to share
example for problem 3 on white board
IV) Classification of
two-dimensional band ornaments: the last
pieces
A)
Add
our examples from homework assignment 15 to above table
B)
The
remaining examples: instructor to do
C) Add the last examples to the
table: hand out visual presentation from
Washburn & Crowe (page 61)
D) Hand out the flow chart from
Washburn & Crowe (page 128)
1)
Team
exercise: teams use the flow chart to
find the type (classification name) and also find what example it is on our
table of examples
2)
Teams
report
Outline
17 continued
V) Symmetry
Fest
A) rules
B) Tournament
1)round one
2) round two
3)
final round
VI) Break
VII) UWB course evaluation
VIII)
Quiz 2 on Wednesday 5/24
A) Review: what will be covered & what you need to
know