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Spreadsheet to Prove that A = pi*r^2

Date: 18 Mar 1995 00:33:39 -0500
From: Anonymous
Subject: pi

I need to prepare a spreadsheet using repetitive calculations 
to prove that A = pi*r^2. HELLLLLPPPPPP!

Date: 30 Mar 1995 11:15:50 -0500
From: Dr. Sydney
Subject: Re: pi

Hello there!

I'm sorry it has taken us so long to get back to you!  What 
kind of spreadsheet were you hoping to make?  

What comes to my mind first as an idea for a spreadsheet 
to prove A = pi r^2 is that you approximate finding the area 
of a circle by inscribing regular polygons with varying 
numbers of sides inside of the circle.  So, your spreadsheet 
could find the area of a circle of radius 1, for instance.  
Then you would want to show that the area of the circle is 
just pi, right?  So, you could inscribe a triangle in the circle, 
then a square, then a pentagon, then a hexagon, etc.... on up to 
a 9999999999999999-gon, if you want.  Do you know how to 
find the area of an n-gon?  If you don't, write back, and we'll
help you.  

Anyway, as the number of sides in the polygon you are inscribing 
gets larger, the polygon's area approaches the circle's area, 
right?  For instance, if you draw a dodecagon (12 sides) inside 
a circle, its area is going to be closer to the area of the 
circle than a square, so you could show that as the number of 
sides of the inscribed polygon increases, the area gets closer 
and closer to pi.

You could repeat this for circles of different radii, for a 
"proof" of sorts. 

I hope this helps out. If you have any more questions, feel 
free to write back!

--Sydney, "Dr. Math"
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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