beyond a number,

ratio, concept; the reason

squares can’t be circles

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just haiku it

the joys and challenges of life, seventeen syllables at a time

beyond a number,

ratio, concept; the reason

squares can’t be circles

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March 14, 2007 at 9:48 am

missjuiceThat’s what I learned today – no square can be constructed whose area is equal to the area of any given circle. And now, the bonus haiku:

writing pi haiku

required research to sound smart

left my brain spinning

i bow to math geeks

even wikipedia

is over my head

March 14, 2007 at 11:02 pm

TanyaOde to ~pi! ðŸ˜€

March 15, 2007 at 11:22 am

missjuiceVerily!

March 18, 2007 at 4:28 pm

maria“no square can be constructed whose area is equal to the area of any given circle”

That doesn’t make sense to me. The area of a circle of radius r is just pi*r^2. So if you have a square with sides of length sqrt(pi)*r it would also have an area of pi*r^2.

Maybe I’m missing something here?

March 18, 2007 at 4:29 pm

mariaI really like the haiku, though! I took the “squares can’t be circles” a different way.

March 18, 2007 at 8:20 pm

elsanne‘Cause you are one!

March 18, 2007 at 10:32 pm

missjuiceBut maria, how can you have a length of sqrt (pi) if pi is infinite… how do you sqrt an infinite number? Something multiplied by itself can’t produce an infinite result. Tell me if I’m missing something.

Besides, wikipedia said so ðŸ˜‰

March 20, 2007 at 10:44 pm

mariaAh, we’re talking about *physical* construction. I get it now. Yes, since Pi is transcendental, we cannot create a physical square that has the same area as a given physical circle. However, in mathematics we deal with things that don’t have good physical analogies all the time, e.g. complex (“imaginary”) numbers. Here is a mathier site’s explanation:

http://mathworld.wolfram.com/CircleSquaring.html

And yes, you can take the square root of an infinite (i.e. irrational) number; you just can’t calculate it perfectly. But we can’t calculate pi perfectly, either. That doesn’t mean it doesn’t exist, KWIM?

Elsanne, something about rubber … and glue … ðŸ˜›

March 21, 2007 at 7:49 am

missjuiceI know what you mean about being able to calculate something perfectly vs. it actually existing. I told you, this stuff kind of made my head hurt. In one particularly spectacular moment, I had myself almost convinced that since pi is infinite, it was actually growing, and therefore all circles were constantly expanding. Dizzymaking. And incorrect, of course, but it was a concept I was trying to grasp.

March 23, 2007 at 12:30 am

mariaInfinity makes everyone dizzy. Even mathematicians. Or possibly especially mathematicians and that’s why they’re so weird and scattered.

I still remember the one that rocked my world: In second year, a prof stood at the board and explained how a particular infinite series can be summed to any number you want, just by changing the order of the elements of the series. I still don’t really get that one.