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SYMMETRY
A Sketchbook of Symmetry
SYMMETRY
• A Definition?
• Symmetry OPERATIONS– Reflection– Rotation– Others
• Symmetry Elements– Mirror (plane)– Rotation axis
SYMMETRY ELEMENTS
• MIRRORS– planes (lines in 2d)– cuts object in half– halves are mirror images– Shown as a dotted line
SYMMETRY ELEMENTS
• MIRRORS– planes (lines in 2d)– cuts object in half– halves are mirror images– Shown as a dotted line
Questions to ask:• Reflective symmetry?
– Where?– Draw mirror(s).
• Rotational Symmetry?– Where is axis?– What fold is axis?– Draw axis.
LILY
HIBISCUS
PLUMERIA
Orchid
Tulip
SNOWFLAKES
• Wilson “Snowflake” Bentley
• Vermont farmer
• His work is world-famous.
• photographing individual snowflakes.
• First photograph
• Over 5000 photographs
• “No two alike”
• http://snowflakebentley.com/
SNOWFLAKES
2 More Examples of Snowflakes from Bentley’s Photographs
From another source...
• Another site:• http://www.its.cal
tech.edu/~atomic/snowcrystals/
Growth of a snowflake…(approx. time was 5 minutes)
Some Further Links to Explore:
• Symmetry of Border Patterns– http://www.math.okstate.edu/~wolfe/border/
border.html
• Symmetry of Inorganic Molecules– http://neon.chem.ox.ac.uk/vrchemistry/sym/splash.html
• Field Patterns– http://mathforum.org/geometry/rugs/
symmetry/fp.html
• END
Symmetry References
• Symmetry of Inorganic Molecules
• Snowflake Bentley
• Great South Catalog
• Other Snowflakes