Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Unit 6

The Beauty of Symmetry

Pattern Wallpaper Pattern

In mathematics, symmetry has more than just a visual or geometric quality. Mathematicians comprehend symmetries as motions—motions whose interactions and overall structure give rise to an important mathematical concept called a "group." This unit explores Group Theory, the mathematical quantification of symmetry, which is key to understanding how to remove structure from (i.e., shuffle) a deck of cards or to fathom structure in a crystal.

Unit Goals

Video Transcript


They say, beauty is in the eye of the beholder. What we consider to be beautiful in nature, art, or music often differs from culture to culture. But somehow, there seem to be constants — commonalities in how we as human beings "see" beauty. Where does that "sense" of beauty and order come from? And what does algebra or geometry have to do with it?



The mathematical study of symmetry is the rigorous study of the commonalities between objects or situations.



Using common motions, such as rotation and reflection, this interactive will introduce the parameters for symmetry groups. You will be able to experiment with wallpaper patterns using their base objects.


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