Transcript Which are the lines of symmetry?

Transformations and
Symmetry
Transformations
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Reflection
Translation
Glide Reflection
Rotation
Scaling (not topological)
A transformation turns a geometric figure into another
by one of the actions above.
Reflection
The blue triangle is reflected across line
m (called the line of reflection).
Translation
Sliding a figure. A translation could be accomplished by
several reflections.
Glide Reflection
The figure reflects across the line, and slides
forward.
Rotation
The blue image is rotated about the
point p.
Scaling
The blue star has been scaled upward by a
multiplying factor. Scaling (changing size) is not a
topological transformation.
Symmetry
•Our basic idea of symmetry is 2-fold
symmetry
•A figure whose halves are mirror images of
each other over a fold line
•We could think of this as being able to
transform half of the image into the other half
by reflection
Which are the lines of
symmetry?
Only m
Which are the lines of
symmetry?
L, M, N, O
Which are the lines of
symmetry?
M, O
Which are the lines of
symmetry?
T,R
Symmetry (II)
• More complicated types of symmetry
arise if we consider objects obtained
from reflection, PLUS other
transformations such as rotation
• Various patterns have been
characterized as symmetry groups
Conway Notation
• Is one way mathematicians use to
describe various symmetry groups
• Can get very complicated!
Kali
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We’re going to look at some symmetry
groups using the program Kali
Keep an eye out for two basic
notations:
– An integer (1,2,3) denotes a
ROTATIONAL symmetry
– An * denotes a reflection as well
KALI
The title picture …
…was created in kali, then colored in with paint
Symmetry in Nature
Chinese Rose
Symmetry in Nature
Crab
Symmetry in Nature
Starfish
Symmetry in Art
Quilt
Symmetry in Art
Pennsylvania
Dutch Hex Sign
Symmetry in Art
Persian Carpet
Symmetry in Art
Ukranian Painted Easter Eggs
Symmetry in Art
Mosaic Tile (Iran,
14th C.)
Symmetry in Art
A Kaliedotile