Equal Areas

By Page Bird

 

Construct a circle that has five regions of equal area where none of the perimeters of the regions can pass through the center of the circle.

 

 

For this problem, I decided to use circular regions.  Before I could get started using GSP, I first had to do some calculations.  The planning went as follows:

 


 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 


As you can tell these models are not to scale and they are not dynamic.  The goal is to create models that are to scale and that are dynamic.

 

I can use the unit circle to create a geometric picture of:


 



 

 

 

 

 


 

 


 

 

 


With the same reasoning, I created lengths that represent the square root of three, four, and five:


 

 

 

 

 

 

 


In the last step, I constructed the circles using the radii as the square root of  1, 2, 3, 4, and 5.  Below is a picture:

 

 


 

 

 


Click here for the dynamic model of this picture.

 

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