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Saturday, November 24, 2012

Pi(e) is a Relationship

 
As noted the other day, there has been no blog proof of pumpkin pie. The mathematical proof of π is simple. In fact, it doesn't need any proof. It just is. It's the relationship of a circle's circumference to the diameter. It doesn't matter if the circle is large or small, if you divide the circumference by the diameter you get π. Exactly. Although there is no exactly, because it's an irrational number, a number that goes on infinitely with the division never coming out even. And it can't be represented exactly by a fraction. When we used 3.14 or 22/7 in high school, those are only approximations that are close enough for most problems.

If you want the area of a circle there's another relationship with π in it, πr2.

Interestingly enough, we've just wandered into calculus. Since d=2r (diameter equals twice the radius), then the circumference = 2πr

If you integrate that "line" you get πr2, and the integral of any line gives you the area under the line.

OK, I almost kept going, but I expect most readers have already had enough math fun for the day.

Pie is a relationship too. It's the relationship of fat, flour and liquid worked into a crust, and some filling, sweetener and thickening, baked to a state of perfection.

pumpkin pie

I'm not about to start complaining about sunshine, so you'll just have to deal with the dappled light in that picture. If you look to the far right, you'll see the filling in the blender. I guess that's the only not-quite-conclusive proof I can offer that it was made from scratch. The crust speaks for itself.

pumpkin pie

I've learned that a 10" pie holds twice as much filling as a 9" pie. How's that for an interesting relationship?

pumpkin pie

The relationship of the size of the pie to the number of servings is also an irrational number. No matter how big the pie is there is never enough and it doesn't come out even.

See Rhubarb Pie
See Crabapple Pie
See Cherry Pie
See Apple Cranberry Pie
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7 comments:

Shelly said...

True. There is never enough pie. I love apple and pumpkin.

Guess what I had for breakfast with my coffee this morning?

Hugs and chocolate,
Shelly

Secondary Roads said...

Oh my,
How your pie,
Catches my eye,
Bet it tastes fi[ne].

Felix Lee said...

You lost me at the math equations but got me back at the pie. I love home-made pies. You're right about there never being enough pie. There's always room for some more.

Ann said...

We are down to one slice left of our pumpkin pie, which by the way does not look nearly as good as yours and wasn't home made. I wonder which one of us will break down first and eat that last slice :)

betchai said...

you made me smile here big time with your transition from pi to pie :) your pie looks so yummy, i believe i ate too much pumpkin pie this past week too :)

Sharkbytes said...

Shelly- Yup, pie for breakfast is THE BEST

Chuck- maybe you'll be a recipient some time

Felix- I'm sure many readers agree with you! Glad you commented.

Ann- The last slice usually gets split

betchai- a very easy thing to do (eat too much!)

Lin said...

Dang! I didn't make pies, so we don't have any at home. Sure could go for a piece right now. :( May have to make one soon--I still have a taste for pumpkin pie. That's the downfalls of going to someone else's house for the holiday--no leftovers. Bummer.

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