Pi by Lauren-Marie Sliter, Alden
December 26th, 2007 12:01 AMThis is pi calculated the old-fashioned way.
Imagine a circle with radius r, and a square where the distance from the center to the middle of one of the sides is also r. The area of the square is then 4r^2, and the area of the circle is r^2 times some coefficient (pi). To calculate pi we must simply compare the area of the square and the area of the corresponding circle.
My sister and I measure the area with dog kibble.
Read on...
Square, circle.
Measuring the square.
Measuring the circle. They both have a radius of about 4" 7/8.
Filling with kibble.
Still filling. We filled each with one layer, attempting to weed out very large and very small pieces.
Pokin' down the kibble.
All full!
Counting. We group them into bunches of 10.
Lot's o' kibble.
Entirely counted! Circle = 441 pieces, Square = 454 pieces
Crappy calculations. Messed up my variables at first. As=4r^2;Ac=(pi)r^2; solve for r^2 and you get As/4=Ac/(pi); solve for pi, 4Ac/As. Which according to the calculator is in this case 3.89! Not bad for dog kibble as Lauren said.
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Archimedes never appreciated the mathematical value of dog kibble. Therefore you are cleverer than he.
Interestingly, I bet there's a perfectly good reason for getting a high estimate. Because you're using round things, you'll have much higher packing density around the edge of the circular basket than around the edge of the square pan. All that wasted space in the pan could fit more kibble if put together, and would lower your estimate for pi.
excellent work.
you have proven how greedy and tiresome squares are, when compared to the efficient, pleasing circle.
i didn't realize that the square and the circle had such strong followings amongst SF0 players. it sounds like the makings of some sort of ridiculous protest.
Indeed, not bad for dog kibble!