symmetry and iteration
Post on 07-Jan-2016
17 Views
Preview:
DESCRIPTION
TRANSCRIPT
Symmetry and Iteration
RM-MSMSP Geometry Project
By Lyndell Kay Thompson
Summer 2006
Consider Daisies in NatureWhat 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
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!
top related