Spreadsheet to Prove that A = pi*r^2Date: 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" |
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