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