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

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Presentation transcript:

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. 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.

Creating Daisies Congruent circles with centers on intersection points

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

Which daisies are different? Explain.

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

Seashells in Nature

What shapes do you see?

Natural Shell Patterns

Spirals have an iterative pattern. 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 P

Creating the seashell

Repeat to create the shell.

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.

A Model of an Iterative Shell

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

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