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Symmetry and Iteration

Symmetry and Iteration. RM-MSMSP Geometry Project By Lyndell Kay Thompson Summer 2006. Consider Daisies in Nature What symmetry do you see?. Symmetry is inspirational. Describe the intersection points. Steps to Create Daisies. Draw a circle.

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Symmetry and Iteration

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  1. Symmetry and Iteration RM-MSMSP Geometry Project By Lyndell Kay Thompson Summer 2006

  2. Consider Daisies in NatureWhat symmetry do you see?

  3. Symmetry is inspirational.

  4. Describe the intersection points.

  5. Steps to Create Daisies • Draw a circle. • From a point on the circle, draw another circle using the same radius. • From the point of intersection of the circles, draw another circle with the same radius. • Repeat to create daisies.

  6. Congruent circles with centers on intersection points Creating Daisies

  7. Why does it work? • The daisies have 60 degree rotational symmetry. • Using the same radius creates equilateral triangles with all interior angles = 60 degrees

  8. Which daisies are different? Explain.

  9. Fill the plane with daisies. Repeat the pattern again and again or create a tool.

  10. Seashells in Nature

  11. What shapes do you see?

  12. Natural Shell Patterns

  13. Spirals have an iterative pattern. P • Construct a segment. • Construct a perpendicular to the segment at an endpoint • Construct a triangle. • Construct a perpendicular to the hypotenuse at point A. • Construct a circle with radius AP. • Use the point of intersection as a vertex to form a new triangle. A

  14. Creating the seashell

  15. Repeat to create the shell.

  16. Iterating to Create the Shell • Create a segment. • Create the right triangle and one point. • Select the points and map the iteration. • Set number of repetitions and iterate.

  17. A Model of an Iterative Shell

  18. A Model of an Iterative Shell

  19. Symmetry and Iteration • In Nature and Geometry • Happy Hunting! • Patterns and Inspiration • True Mathematics

  20. Au revoir mes amis! Dommage! C’est la fin!

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