SYMMETRY: SYMMETRY: Theory, Reality and Theory, Reality and Art!Art!

A GEMS/ALEX SubmissionA GEMS/ALEX SubmissionSubmitted by: Elizabeth Thompson, Submitted by: Elizabeth Thompson, PhD.PhD.Summer, 2008Summer, 2008

Types of SymmetryTypes of Symmetry

•Rotation

•Translation

•Reflection

Rotational SymmetryRotational SymmetryIllustration: http://mathforum.org/sum95/suzanne/symsusan.html

Take an object and rotate it by some degree (90, 45, 180, 26) and you have an example of ‘rotational symmetry)

Every rotation has a center and an angle!

Examples of Rotational SymmetryExamples of Rotational Symmetry

Can you find the center of each object, and approximate the degree’s that each object was rotated? (click for each)

What other objects would have rotational symmetry?

Translational SymmetryTranslational Symmetry

Illustration: http://mathforum.org/sum95/suzanne/symsusan.html

Every translation has a distance and a direction.

Translations are not rotated or reflected…the shape remains the same size.

Examples of Translational Examples of Translational SymmetrySymmetry

The objects simply move from one position to another retaining size and shape.

Reflective SymmetryReflective SymmetryIllustration: http://mathforum.org/sum95/suzanne/symsusan.html

Every reflection has a line of reflection (a mirror line).

Examples of Reflective Examples of Reflective SymmetrySymmetry

Can you find the line of reflection in each object? (click to see)

Multiple forms of symmetry can be Multiple forms of symmetry can be found in one object…can you name found in one object…can you name the ones found here?the ones found here?

The flower has rotational and/or reflective symmetry.

The Escher Art has reflective…then it is translated (that makes it a tessellation)

POWERPOINT BREAKPOWERPOINT BREAK TIME FOR PRACTICE TIME FOR PRACTICE

(see teacher notes)(see teacher notes)

PART TWO: TessellationsPART TWO: Tessellations(Geometric Art)(Geometric Art)

"I never got a pass mark in math ... Just imagine -- mathematicians now

use my prints to illustrate their books."

-- M.C. Escher

Samples of tessellationsSamples of tessellations

How to Tessellate (Slide 1 of 3)

(there are many methods…this is just one)

How to Tessellate (Slide 2 of 3)

How to Tessellate (Slide 3 of 3)

Student Samples (repeated)

Warning: These are harder than they appear…frustration levels can rise.