symmetry and iteration
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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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/1.jpg)
Symmetry and Iteration
RM-MSMSP Geometry Project
By Lyndell Kay Thompson
Summer 2006
![Page 2: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/2.jpg)
Consider Daisies in NatureWhat symmetry do you see?
![Page 3: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/3.jpg)
![Page 4: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/4.jpg)
Symmetry is inspirational.
![Page 5: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/5.jpg)
Describe the intersection points.
![Page 6: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/6.jpg)
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.
![Page 7: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/7.jpg)
Creating Daisies Congruent circles with centers on intersection points
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Why does it work?
• The daisies have 60 degree rotational symmetry.
• Using the same radius creates equilateral triangles with all interior angles = 60 degrees
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Which daisies are different? Explain.
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Fill the plane with daisies.
Repeat the pattern again and again or create a tool.
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Seashells in Nature
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What shapes do you see?
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Natural Shell Patterns
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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
![Page 15: Symmetry and Iteration](https://reader035.vdocument.in/reader035/viewer/2022062517/56813eda550346895da94c69/html5/thumbnails/15.jpg)
Creating the seashell
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Repeat to create the shell.
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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.
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A Model of an Iterative Shell
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A Model of an Iterative Shell
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Symmetry and Iteration
• In Nature and Geometry• Happy Hunting!
• Patterns and Inspiration• True Mathematics
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Au revoir mes amis! Dommage! C’est la fin!