
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 1st2nd
grade multiage 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



start

step 2

final product

[B] 5 Points around a circle & Rule: skip 0


second line

final product

[C] 6 points around  Rule: skip 1


This will be the actual result.

What change in the rule will give this preferred result?

[D] 6 points around  Rule: skip 2


This is both the first and the actual result, and, of
course every step in between.

What rule change will give you this result?


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