Stars and Polygons
Purpose: promote interest in geometry, demonstrate the connection between geometry and group theory (clock groups), discover a diagram to promote the concept of infinite progressions.
Background: this lesson was used successfully in a 1st-2nd grade multi-age classroom setting. Students enjoyed drawing the different patterns and discovered the relationship between the pentagon and pentagram on their own.
Written 2001:
Reformatted: January 2010
Introduction:
The following steps may be Introduced:
- Arrange points around a circle.
- Create a simple rule for going from one point to another, such as skip a point.
- Draw in lines that follow your rule until you reach your starting point
- Describe your results. Compare your results to other rules.
Examples:
[A] 5 Points around a circle & Rule: skip 1
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start |
step 2 |
final product |
[B] 5 Points around a circle & Rule: skip 0
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second line |
final product |
[C] 6 points around - Rule: skip 1
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This will be the actual result. |
What change in the rule will give this preferred result? |
[D] 6 points around - Rule: skip 2
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This is both the first and the actual result, and, of course every step in between. |
What rule change will give you this result? |
Related Pages at this site
Questions:
- How are all these results similar?
- What do you think makes each one different? How can you test your conjecture?
- What rules will give you a polygon, a star, a line?
- When will two different rules give you the same picture?
Extensions:
This lesson may be expanded to visually present the idea of an
infinite progression.
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Notice how when we put the skip 0 rule and the skip 1 rule together we get the pentagon inside the pentagram inside the pentagon. This sequence may be extended ad infinitum - in the class room drawn ad nauseum.. |
This lesson may be used to demonstrate addition in clock groups. For example: If it is now 10:00 what time will it be in 5 hours? |
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