Math Help!

[mlujan]

I'm trying to find out what is the best way to find the area of a circle w/o using pi or the formula for it..

any ideas???

 

i read something about polygons.. are there other methods?

[hotcommodity]

Think of using 2 squares, one bigger than the circle, and one smaller. How would the area of the circle relate to the area of the two squares?...

[insane_alien]

you could do it through integration. do you know much calculus?

[Bignose]

Way back when, they would calculate the area of regular polygon inscribed and circumscribed to the circle. There are formulas you should be able to find or look up to calcuate the areas of regular polygons. I know I read about some monk who spend his whole life doing the calculations for something like a 20 million sided regular polygon.

 

However, on a more practical note, I have an interesting idea. Find a piece of paper that you have several of the same sheets of the exact same kind. Use a ruler and a corner to cut out exactly one unit square of that paper, say exactly one inch squared or one cm squared. Actually, you probably want to do this several times, like 10 so that you get a good average (since it is difficult to get exactly one square unit). Now, weigh those squares so that you know the weight of one unit square of that paper. You're going to need a pretty accurate scale, some kitchen scales are acurate enough. Next, trace out lots of circles using a compass, all the same radius, and weight those. The average weight of those cut out circle divided by the average weight of the unit square will give you the average area of the circle. Then you can get pi.

[the tree]

If you take the area of a regular n sided polygon inscribed to the circle, then as n tends to infinity the area will tend toward that of the circle. Although, for large n, it's difficult to find the area without using pi so the best you'd come up would be a sloppy estimate rather than an accurate limit.

If a sloppy estimate is all you're looking for then you could just draw a polygon that roughly matches the circle and apply Pick's Theorem to find the area of that, but that wont be much better than a guess.

 

What exactly are your reasons for wanting to do this?