Saturday, March 14th, 2009 Three Point One Four One Five... Nine Two Six Five Four...
Annnnd that's all I know. More than some, a lot less than others.
Happy friggin' PI DAY, people. The day where we celebrate the majesty of numbers, specifically irrational ones.
Two presents for you:
First, a story.
Once upon a time there was a man called Pythagoras. Pythagoras was a brilliant man, but he was also a rather fanatical man, and created what was basically a religion around the study of mathematics. Being also a very VAIN man, he named his group of merry men the Pythagoreans.
Now, the Pythagoreans believed one thing more than any other: all numbers could be expressed as the ratio of two integers. Now that's just a fancy way of saying that any number you can think of can be written as a positive or negative number (without a decimal part) divided by another such number. 5.23? Why that's just 523 divided by 100! 12.9146? That's just 129146/10000!
And so, the Pythagoreans traveled from place to place, spreading the word of All Holy Math to people who probably nodded politely and then rolled their eyes after they had left.
One day, as the Pythagoreans traveled on a boat from one Greek city to another, a man named Hippasus sat on the deck of a ship with parchment or whatever the heck the Greeks used to write on (I'm not a historian, people!). He was playing with the also-vainly named Pythagorean Theorem and said to himself "Well, we know that a right triangle with two sides of length 1 must have a longest side of length the square root of 2, so such a number has to exist..."
He scribbled on his parchment and after he was done, his eyes grew wide...he had just proved, beyond a shadow of a doubt, that the square root of two could NOT BE EXPRESSED AS THE RATIO OF TWO INTEGERS! THEY HAD BEEN WRONG THIS ENTIRE TIME!
He rose excitedly. "My brothers, look what I have done!" He showed one man, then another and another his perfect proof.
Each one looked at him thoughtfully. The nodded and rubbed their beard with their hands as all important, bearded men are wont to do.
And then they threw him off the boat.
And this, my friends, is the story of the first truly irrational act of murder.
Speaking of π, I read about how, given an infinite number of parallel lines on the ground, and if you randomly drop needles (or sticks I guess) of the same length as the space between the lines, the probability of a needle crossing one of the lines is 2/π.. The proof is pretty cool.
Even more interesting, but less relevant, I also read about the proof that there can be one infinity larger than another. Fascinating, simple, yet ingenious. I might write a blog on that one because it's so fascinating.LimeyGeorgeSaturday, March 14, 2009
2) Limey, you're right about the probability "experiment". Actually, by the Law of Large Numbers, if this experiment were conducted an infinite number of times, we would get the infinite string of digits of pi. As it is, we can do the experiment some finite number of times and get a damn good aproximation for pi.
And yes, you're right about different "sized" infinities. In layman's terms, if you have the set of real numbers and the set of integers, clearly they're both infinite sets (Want a higher integer? Add 1. Want a new real number? Find the halfway point between two real numbers you already have.) Also, it's pretty obvious that, in SOME sense, there are "more" real numbers than there are integers. The study of what the heck "more" means in this case is why we have weird things like different sized infinities.ScottSaturday, March 14, 2009
3) Would love to read it, George.stheinzSaturday, March 14, 2009
4) I should have added, that as far as *proofs* go for both of these concepts, they're probably both above my head.ScottSaturday, March 14, 2009
5) Actually both proofs are quite simple. I've done far more complex proofs myself. These ones are intuitive rather than abstract.LimeyGeorgeSaturday, March 14, 2009
6) haha I don't know where, when or why...but I have seen that video before!!AmberMonday, March 16, 2009
7) Pi is actually calculated to be 3.14159, only non mathematicians and non engineers use the shortened version. As an Accountant, we used the long version because some of the parts that were being costed were to such tolerances the longer version was used to get very accurate costs.BeanCounter37Monday, March 16, 2009
8) Pi is infinitely long.
Why would anyone use pi to calculate accounts anyway?ScottMonday, March 16, 2009
9) I use it to calculate those circular references on my spreadsheets.Good NewsMonday, March 16, 2009
Speaking of π, I read about how, given an infinite number of parallel lines on the ground, and if you randomly drop needles (or sticks I guess) of the same length as the space between the lines, the probability of a needle crossing one of the lines is 2/π.. The proof is pretty cool.
Even more interesting, but less relevant, I also read about the proof that there can be one infinity larger than another. Fascinating, simple, yet ingenious. I might write a blog on that one because it's so fascinating.
And yes, you're right about different "sized" infinities. In layman's terms, if you have the set of real numbers and the set of integers, clearly they're both infinite sets (Want a higher integer? Add 1. Want a new real number? Find the halfway point between two real numbers you already have.) Also, it's pretty obvious that, in SOME sense, there are "more" real numbers than there are integers. The study of what the heck "more" means in this case is why we have weird things like different sized infinities.
Why would anyone use pi to calculate accounts anyway?