Day 8 : Make Figures with
7 types of Strip Pattern Symmetry
by Jongsuk Keum
Goal
Students explore 7 types of strip pattern,
make the multiplication table, and make figures for the strip pattern using
GSP.
Multiplication table for
Strip Pattern
A detailed multiplication table for the types
of isometries which occur as symmetries of strip pattern. Let
L be the center line of a strip pattern. Make a table for the types
- I = identity
- T = translation
with vector parallel to L, T not the identity
- R = rotation
with center on L and angle 180 degrees
- V = reflection
with "vertical" mirror, i.e. mirror perpendicular to L
- H = reflection
with "horizontal" mirror, i.e. mirror L
- G = glide
reflection with mirror L, G not equal to H
|
I |
T |
R |
V |
H |
G |
| I |
I |
T |
R |
V |
H |
G |
| T |
T |
T,I |
R |
V |
G |
H,G |
| R |
R |
R |
T,I |
H,G |
V |
V |
| V |
V |
V |
H,G |
T,I |
R |
R |
| H |
H |
G |
V |
R |
I |
T |
| G |
G |
G,H |
V |
R |
T |
T,I |
Seven types of strip pattern
T, TR, TV, TG, THG, TRVG, TRVHG
Conway's names for strip pattern
1. Hop ( T )
2. Spinning Hop ( TR )
3. Sidle ( TV )
4. Step ( TG )
5. Jump ( THG )
6. Spinning Sidle ( TRVG )
7. Spinning Jump ( TRVGH )
Homework
Make figures of 7 types of
Strip Pattern symmetry using GSP
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