Friday, March 14, 2014

day 17 pi day

All about pi on a very social Friday.

So today is March 14, or 3.14 in America. In Europe, it would be 14.3 and Europe can never have a pi day, as there are not 14 months. Europe could have a pi month, this month March as it is 3.14 this year but this is the last time for a hundred years in Europe whereas we here in irrational America can have a pi day every year, as we do the month before the day, and then the year, which is not logical. Europe is more logical, as you should go from days, to months, to years.

Okay, now let's consider pi. Pi is the ratio of the circumference (c) to the diameter (d) or c/d = 3.1416...


You should be able to calculate it by putting a string around the C, measuring the C, and measuring the D and dividing. So we tried that.

Unfortunately, we only got 2.85, which is pretty far off. Pulling the string? Missing the center point of the circle? Counting the squares wrong? Something went wrong. 


Anyway, why is this particular ratio magic? The equivalent of the diameter of a circle in a square is a single side.

So you see, four sides is the C and one side is the D: 4/1 = 4.

Now as we add sides from 4 (a square) to infinite sides (a circle) we should see the ration drop from 4 to 3.1416... Look at 6 sides:

I didn't bring a compass so you should kind of see the sketched bad circle I drew on the paper in the middle of the six sided shape with the idea that the circle only touches the polygon six times and that the two shapes (the circle and the hexagon) have the same center point. 

Here, just doing it rough on the wall, the side of the hexagon was 60 (6 sides, 10 cm each) and the D was 16. 60/16 was 3.75, which is between 4 and 3.1416... but closer to 4. 

See all the shapes behind the people playing cards? Those are polygons, from 4 sides, 6, sides, 8 sides, etc... Going towards the circle. 

As you measure the ratio, it should decline and approach a number from which it will stop declining... which would be pi. 


This would have actually been better for calculating with unpopped popcorn, but it would not have been as tasty. 

So, we draw a big square on the paper. And then put a circle in the middle. The area of the circle should be pi*r^2 and the area of the square should be 4•r^2. As the r^2 cancel, the area of the circle and the square would be proportional pi/4 is like circle over square. 

So throw the popcorn over the paper and then count the popcorns. 

We failed again. But we got exactly the same wrong number. 

So then Bridgette brought a project to ask everyone about certain genetic characteristics, hitch hiker's thumb, whether your big toe is bigger than the seond toe, etc. 

We anxiously await the pie charts showing the results. 

Then we ate pie.

Then we went to the doctor and saw a poster about all the hazards in the world and came home and took a picture of a hazard they forgot: a van falling off a jack. 

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