I did an irrational thing today, with a slice of key lime Pi.

[MineralMan]

I tried to cut exactly one-sixth of the pie, but could get a real number for my measurement, no matter how many decimal points I used. So, I cut and ate an irrational piece of pi. It was good, but I'm still struggling with the imprecision of it all.

[a kennedy]

1. Happy national Pi day to you.

[MineralMan]

3. Will it go round in circles?

That's the question. And why is the relationship between a circle and its radius irrational? That question has troubled me since the first time I used a compass to try to divide a circle into six equal parts, back in grammar school.

I know that most people don't think about such things, but I've been thinking about that ever since. One can draw a perfect circle with a compass, but you can't divide that circle into 6 parts. You also can't generate a perfect 60 degree angle with instruments.

Nor can you trisect a line using geometry. It's all whack.

Such are the things that occupy my mind today.

[Jim Lane]

14. Mathematical correction

You write:

You also can't generate a perfect 60 degree angle with instruments.

I disagree. There is no general procedure that will enable you to trisect angles, but in the special case of a 180-degree angle, you can trisect it by constructing an equilateral triangle. See explanation of steps here.

(I'm assuming that your phrase "with instruments" means compass and straight edge, the classical tools.)

Whether this method could be used to divide a pie into six equal pieces is left as an exercise for the reader, and you'll certainly need some exercise after eating all that pie.

[OldHippieChick]

2. I hate eating irrational pieces.

[MineralMan]

4. Yes. that's why my sister always ended up with a bigger

piece than I did in our family of six, I'm certain. It's totally, you know, unfair.

[MineralMan]

5. Another excellent question about Pi:

Why is a hexagon such a common thing in nature? There are perfectly hexagonal crystals of many minerals. Bees build perfectly hexagonal cells in their comb, and so on. Yet, humans cannot divide the circumference of a circle into six equal parts.

Go figure. But, no matter how much you figure, dividing by multiples of three doesn't work in geometry, despite the number of degrees in a circle is easily divisible by multiples of three, such as six and nine. I can, for example, create a perfect octagon by bisecting lines with a compass, but cannot create a perfect hexagon, not matter what I do.

'Tis a puzzlement. I'll die never knowing why that is.

[OldHippieChick]

7. Now you have me pondering

pentagons and their divisibility.

[MineralMan]

9. Yah, pentagons, too.

They're a standard face on some crystals. However, there is a way to create a perfect pentagon with a compass and a straightedge. But not a hexagon. No way to do that.

[panader0]

6. Eat the entire pie.

Then your only struggle will be with a bellyache.

[MineralMan]

8. Oh, I will. I will.

But in time. That pi is mine!

[planetc]

10. The key decision (forgive me) was to choose a key lime pie.

Every crumb is delicious. I would not have bothered with pi, but would have measured, say, a quarter of the pie and divided by something.

[MineralMan]

11. Yes. I was torn between a chocolate cream pie

and the key lime one. I really enjoy both. But, my doctor said I should eat more fruit.

[planetc]

12. Doctors always say that.

I don't say they lie, but I bet if you asked them to cite the study, they'd have a hard time. While they're worrying about that, you can get another key lime pie!

[monmouth4]

13. It's also Albert Einstein's birthday! I love pie..n/t