The document discusses two types of symmetry found in nature: bilateral symmetry and rotational symmetry. Bilateral symmetry refers to shapes that can be folded along an imaginary line so that opposite sides match, like many insects and animals. Rotational symmetry involves shapes that look the same when rotated around their central point, exemplified by snowflakes, flowers, and starfish. The document provides examples and images to illustrate these two fundamental forms of symmetry exhibited in the natural world.

1. Mather Nature A Focus on Symmetry in Nature Music: “ Emptiness” by Blu May available under Creative Commons license.

2. The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. -Aristotle

3. Two Types of Symmetry

4. Bilateral Symmetry

5. Image by Davekav available through Flikr under Creative Commons license .

6. Rotational Symmetry

8. Symmetry in which a shape can be folded along an imaginary line (axis of symmetry) so that opposite sides of the shape match Bilateral Symmetry

9. Also called reflectional symmetry Bilateral Symmetry Image by Andrew_D_Hurley available through Flikr under Creative Commons license. .

10. Bilateral Symmetry Images by Adam Pniak, neeZhom, and Tomi Tapio available through Flikr under Creative Commons license. .

11. Symmetry in which a shape can be rotated around its center point so that it looks like its original self Rotational Symmetry

12. Also called radial symmetry Rotational Symmetry Image by Desirae Nelson available through Flikr under Creative Commons license. .

13. Rotational Symmetry Image by Alex Clark, Julie Falk, and Shawn Econo available through Flikr under Creative Commons license. .

14. Review the two basic types of symmetry: Bilateral Symmetry Symmetry in which a shape can be folded along an imaginary line (axis of symmetry) so that opposite sides of the shape match Also called reflectional symmetry Examples include insects, animals, reflections in ponds Rotational Symmetry Symmetry in which a shape can be rotated around its center point so that it looks like its original self Also called radial symmetry Examples include snowflakes, flowers, starfish