I've never liked Pi. In school I was told that it was 3.14 and I remembered after school that it had something to do with circles and that it went on forever but there my understanding ended and I was lost.
Until recently when I decided to do a bit of reading and saw Pi expressed not as 3.14 but as 22/7.
Wait a minute. 22/7? With the circumference as the numerator and the diameter as the denominator?! You mean all this time Pi was just a freaking ratio that expressed how big the circumference was in relation to the diameter of any given circle?!?! And THAT'S why you'll get the circumference if you multiply the diameter by 3.14?!?!?
Holy crap! In an instant I understood what 6 years of junior high and high school and 35 years of living hadn't helped me understand just by seeing Pi in fraction form rather then decimal form. All those time when Pi was just presented as 3.14, when stupid news stories went gaga over the discovery of the next digit in the sequence or mathematicians sighed over the beauty of it's irrationality and all the romance and affection glossed over the fact that all a person needed to know about Pi was that it was a constant ratio. 22/7. Period.
Sheesh.
6 comments:
Well, when you put it that way, it actually DOES make a lot more sense, doesn't it? Not sure what kind of left brain/ right brain/ no brain that makes me, but it definitely sounds a lot more understandable that way!
Yep. That's pretty much it. Unfortunately, 22/7 gives us: 3.142857 which then repeats, so it's only a rough approximation [smile]. But if that clears it all up for you, rock, rock on! I'll need to keep that in mind, because, yeah, it's easy to forget that this particular "mathematical constant" actually has a very reasonable source...
~Luke
Ohhh, try this. Write out the doubles of multiplication (1X1, 2X2,etc.) Now look at the products and see the pattern they make. My daughter did this on the driveway and found the pattern, I had never noticed it before.
Luke - Yep. I forgot the approximation bit in my post - that 22/7 and 3.14 are approximations of pi, not exactly pi. An important thing to remember. Regardless, now that I understand how we came up with pi I find I'm starting to understand some of the interest people have in the number and irrational numbers in general.
Liese, I did that at one point last year and noticed that the difference between the products of consecutive doubles (or squares of consecutive numbers) was a the sequence of odd numbers. Draw the squares as dots and you'll see why that's so.
I just wrote down some squares and wondered if you meant the sequence 0,1,4,9,6,5,6,9,4,1,0... in the ones place. That's nifty as well!
Oh yeah sure. Make me read a math post at 7am. :-P
Have you heard the PI song? Christopher loves it - he loves numbers - and I wish I could find as a dl somewhere!
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