August 14, 2005

• There are mathematical objects called "vectors," that, roughly speaking, are used to indicate a point in space, or a direction and speed of travel. Like any mathematical objects, there are times when we want to talk about them, when we don't know what they are. So we give them names. Sometimes we name them with letters like "A" or "x", and sometimes we name them with greek letters, like "pi" or "gamma". The google search just gives some instances of people having a particular vector whose name is pi. (Either that, or they're taking a vector and rotating it some multiple of pi radians.) So really, it doesn't mean anything, just like the terms "number x" and "function f" don't mean anything in particular.
• Oh... Crunchy Frog, do you mean that the "pi" in "vector pi" does not refer to 3.14..., but to the Greek letter "pi"?
• I might owe A. a kiss then. Not that he'd take it. Girl germs, yuck!
• Right. In most of the first twenty results, the term "vector pi" simply means "some unknown or variable vector, which is named 'pi', as in the Greek letter." In a few of them, they say something like "we rotate the vector pi radians". This is just a use of radian measure. (pi radians = 3.14 ... radians = 180 degrees).
• Many thanks, Crunchy Frog, for clearing up a minor mystery that's been plaguing me all day (^_^) Have a banana! )
• Me loves the movie.
• I loved the book as well. Ok, gonna shut up now.
• Neat! One of the links referenced tells you where in pi your birthdate is. But the bestest, most interesting thing about pi for me is this: e**(i*pi) = -1 (e the base of the natural logarithm, raised to the power of i, the square root of -1, times pi ends up being negative one! Which explains the universe and why your socks are red!).
• my socks are green as any leaf in spring they prefer to hide inside a shoe, a drawer, a washing machine their little world is rounded by some sort of box aa mine seems circumscribed by missing socks
• mmmm - Banana Cream Pi
• So, Alnedra, what was this conversation about? I'm a math bachelors and while I'm certainly not worthy to clean the shoes of a doctorate, have some guesses that "vector pi" is either a 180 flip, or is just some random vector with label Greek letter pi. Just in case their vector math wasn't confusing enough... just like Crunchy Frog said. Unless it's something special and is some sort of shibboleth in whatever discipline you were talking about. StoryBored, my favorite version of that equation is: e^(pi*i) + 1 = 0, as it includes five of the most fundamental numbers in mathematics all relating to each other: e, pi, i, 1, and 0. Another fun one involves the number of the beast and the golden mean, phi: phi = -2 sin (666) ... which is vaguely mystical until you figure out that 666 degrees ends up being the bottom foot of a pentagram centered on the origin, and phi is always involved with pentagrams. And then pentagrams are mystical until you figure out that Venus, the brightest star/planet, traces out a pentagram in the sky every eight years since the earth and it are in resonance orbits. And ancient folks surely noticed this, since they noticed the 19 year solar/lunar resonance. And this all may get mystical until you study orbital dynamics and notice that orbiting things really like to form resonances... Then there's that guy who thinks we really should be using 2pi instead of pi, since pi is based on the diameter, and it should more logically be based on the radius. Which is why 2pi shows up everywhere instead of just pi... /mathgeek
• Wow, fatoudust, that is some cool information. Phi and pentagrams, eh? No it just came up in some totally random way. Something about drawing a line under pi or something.... orbiting things really like to form resonances... The more I learn about the universe, the more awed I am. It seems to be alive, even at a planetary level.
• pi is exactly 3. Signed, US miltary-backed big guns and planes and ships. And who are you to say different? Wuss. Irrational numbers? (Right) Sounds pretty hysterical. Like the left always is. Pussies.
• Whoa, that Venus/pentagram stuff is freaky! (Okay, so maybe it's more like Satan's spirograph...) Sent the pi/birthday link to a buddy of mine, turns out he wrote a paper (PDF) on this very subject. Specifically, it's much easier to compute the location of a string of digits in an irrational number than it is to actually compute the irrational number out to that many digits. Same fella also created (AFAIK) my favorite math joke: Q: What's the square root of 69? A: Ate-something.
• Sludge: I first heard that joke in 1981.
• Bees, i put on my math hat And to my dismay Find an error in what I say. Your socks are not red, according to pi. It's your poems that are read And not just by I.
• Fatou wrote: e^(pi*i) + 1 = 0 I've seen it written that way, but somehow it seems less concise. I jettison the zero in favour of compactness! :-) Re: the Phi/666 connection. That's pretty neat and the first i heard of it, thanks for mentioning. This is an artifact of using the 360-degrees-in-a- circle system right? But speaking of mind boggling connections, this one is right up there: E=mc^2.
• rocket88: S'okay -- he didn't write the paper, either. D'oh!
• Hey, I came accross this related link the other day when i was building some trim for my bathroom: specifically, the concept of "poly pi". Or, how to compute the inner diameter and side length of an n-gon. Neat stuff.
• I like pumpkin! Oh, wait. Were you discussing something here?
• Getting pi-faced, I think, BkueHorse.
• Okay here's another neat little thing we can do with e^(i*pi) = -1 Take the square root of both sides: e^[(i*pi)/2] = i Now raise both sides to the power of i e^[(i*pi)/2]^i = i^i and simplifying gives: e^(-pi/2) = i^i What this says is that the result of raising the square root of -1 to the power of the square root of -1 (both imaginary numbers) is *not* imaginary. Isn't that COOOOOOOOL? *greeted with silence* Um, so what's this pumpkin doing here?
• fatodust: "Then there's that guy who thinks we really should be using 2pi instead of pi, since pi is based on the diameter, and it should more logically be based on the radius. Which is why 2pi shows up everywhere instead of just pi..." if pi is related to the diameter, wouldn't (1/2)pi relate to the radius as opposed to 2pi??? where does 2pi show up anyway??? (trying to gleen some more mathgeek info from the room)
• Re: the Phi/666 connection. That's pretty neat and the first i heard of it, thanks for mentioning. This is an artifact of using the 360-degrees-in-a- circle system right? Yep. It's much less fun using grads or radians. Then again, there are some tin-foil-hat theories about "secret knowledge" the "ancients" had and just why the 360 degree circle came down to us from the Babylonians. StoryBored, actually, i^i has an infinite number of real solutions, but yours is the smallest. When you do complex exponents, you can think of the solutions lying on a spiral going out to infinity. i^i is unusual in that all of them lie on the real number line. gonzo, I think you're going in the wrong direction. If pi is the ratio of the diameter of the circle to the circumference, then the diameter fits around the circle 3.14+ times. If we redefine it to use the radius, then it would fit around the circle 6.28+ times, or 2pi. 2pi occurs all over the place when you calculate using radians, since 2pi radians is a whole circle. Anything involving rotation, waves, electronics, phase, and so on. The factor of two is because in modern thinking it makes sense to define circular things in terms of the radius, but we're still using a pi based upon the ancient Greek thinking based on diameters. Let me know if this still isn't clear.
• crystal. thanks.
• i^i has an infinite number of real solutions I'm confused... isn't i exactly one number, sqrt(-1) (let's disregard +/- for now)? Why would i^i have solutions?
• techsmith asked: "i^i has an infinite number of real solutions I'm confused... isn't i exactly one number, sqrt(-1) (let's disregard +/- for now)? Why would i^i have solutions?" It is really weird and counterintuitive, but, yes, when you raise numbers to complex powers, you get an entire series of results. Complex numbers behave in ways that ordinary real numbers could never imagine. Which is one of the reasons that people find them so darn useful. The too-simple answer is that complex powers are defined by complex powers of the number e, which are also used to define sine and cosine functions, so complex powers end up being both periodic and exponential. i^i bounces back and forth between positive and negative, and gets large very quickly. Other complex powers spiral outward in an exponential spiral that gets huge quite quickly. For a more complete answer, here are some links: Here's Dr. Math's take on the topic. Wikipedia's info MathWorld another another Hope this helps, and sorry for the off-topic, but I can't resist a math question.
• I meant to comment on this earlier, but Lord Sludge, the link from the Masons you provided is just *so* full of it! It was a cool link, and thanks!, but they're so trying to deflect attention from the obvious. They claim that Venus couldn't have been the source of the pentagram because Venus isn't visible when it's in conjunction with the sun. Like they weren't smart enough to connect the dots. The ancients surely understood the concept of conjunction because they kept very careful records of solar and planetary movements, and it was obvious to them when planets moved close enough to the sun to be invisible. Heck, several ancient peoples detected the precession of the equinoxes, a cycle which takes over ten thousand years. Venus is the brightest "star" in the sky, and it moves very interestingly and very regularly. Anyone who paid attention to it would discover a pentagram. The pentagram is the first interlocked "star" figure which geometry offers, and is doubly interesting. Not surprising that it became significant.
• It is really weird and counterintuitive, but, yes, when you raise numbers to complex powers, you get an entire series of results. Wow, even COOLER! Thanks for those links fatoudust, and no apology needed for the sidetrack. I'm a comp.sci. major so this is new and fascinating for me. From the link you provided is this interesting money making opportunity: 1^(1/2*pi*i) = e So go up to your well-educated (but non-math majoring) friend and wager that 1 raised to an exponent is sometimes not 1!
• Although, this is in pretty much the same sense that 1^(1/2) = -1.
• Um, 1^(1/2) = 1?
• Both are correct. Written differently, 1^2 = 1 and (-1)^2 = 1 are both correct.
• You can tell i haven't been at the math recently. Rocket and flongj you're right. I should change the original wager and make it more mysterious by challenging them to find an exponent that makes 1^x greater than 1!
• StoryBored, if you study a little complex math, you could make the bet, "Gimme a number, any number! I'll find the solution where I can take one, and raise it to that power, and get your number!" Then again, in a bar, that's far less likely to get takers than, "I'll bet I can toss this dollar bill in the air and predict which side's up!"
• [for a bar bet] "Gimme a number, any number! I'll find the solution where I can take one, and raise it to that power, and get your number!" You say that, you're lucky if you don't get your underwear handed to you. rrrriiiiip!
• "I'll bet I can toss this dollar bill in the air and predict which side's up!" Hey, I don't know this one! You say that, you're lucky if you don't get your underwear handed to you. rrrriiiiip! Remove underwear before issuing bet. Place underwear on bar. Issue bet. Collect money.