I, new member Parameter Π², must ask some most-serious questions about my own identity.
First, I have read the Moderator’s comments about General Questions: I have no opinions; I also have no conclusion to debate. So, it seems, General Questions is the place for these questions.
My questions:[list=1][]Usually “Pi” is not thought of as a parameter. Is it a parameter or just a fixed constant?[]Usually the exponent “2” is likewise not thought of as a parameter. Is it a parameter or is it, too, just a fixed constant?Most telling for students of Physics and Chemistry: Is Π really squared? Or is the exponent something really, really close to “2” but not exactly “2”?[/list=1]I have questions but does anyone have any answers.
My Webster’s says a parameter can be a fixed constant so the answer to question 1 is “both” same applies to question 2.
As for 3 I’m not making heads or tails out of it without a context. Is pi squared? Well if you square it, then it is. What you have is an expression. You may need to equate that expression to something in order for the question to have meaning.
Welcome to SDMB. For my money you’ve made the most baffling first post I’ve ever seen.
Ah. Thanks to you, Padeye, from yours truly, Parameter Π². (Sorry for the pomposity: Couldn’t think of how else to get my handle to come out right.)
Webster is, of course, correct. Usually, however, when a constant is used in the sense of a constant, it is not called a “parameter”, which is usually something that can assume different values.
For example, most people would take “pi” or “Pi” to be a universal-type constants. Would anyone think that there might be some other value for the ratio of a diameter of a circle to its circumference?
Likewise, in the Law of Gravitation, WHO might question the value of the exponent “2” in the denominator to suggest that it might occasionally–maybe on Jupiter–be “3” or even “2.5”?
As to your second paragraph, Padeye, I would prefer not to be specific as to the location of the expression “Π²”. All for the best, though, I suspect. Sorry for the ambiguity; but thanks for the welcome!
I will answer #3, assuming it means something like “In physics and chemistry equations that use the term pi-squared, is the exponent actually 2, or something very close to 2?”
If that is the question, then the answer is: To the degree of precision we can measure, 2 is the exact exponent.
If your question is “Are the laws of physics the same in all locations” then the answer is yes, to the best of our ability to determine, they are. Gravity always falls off with the square of distance, here or on jupiter.
I’m curious as to where pi squared is even used in physics. Maybe I just didn’t take the right classes in college, but I always though that you squared or cubed the radius and multiplied by a single power of pi. Pi squared would be roughly 9.87 - is this used anywhere in physics or chemistry?
It’s easy to trademark the name “Google,” while real words are hard. Now that MS is finding out the hard way when they sued Lindows for trademark infringement.
No, no, AndrewL. I was just citing the thought that the Universal Law of Gravitation might be different on Jupiter than on Earth as a silly thought. Although that thought is one of the fundamental worries that theoretical Physicists have expressed; if I recall correctly, A. Einstein for one, deBroglie for another, have raised this very issue.
I wasn’t asking that particular question; I was just giving examples of why one usually does not think of “Pi” or “2” as parameters.
My questions were: Are “Pi” and the exponent “2” fixed constants or are they parameters?
I believe that you, AndrewL, muttrox, and even CurtC, might be confusing the symbols “Π” and “π”. My question is about the expression “Π²”; the usage of which I do not feel at liberty to discuss.
Ah, Urban Ranger, could the exponent be “1.9999999936…”? Some very urgent matters have been recently decided on much larger variations than this “±0.00000001” example. I’m not suggesting anything, however.
You seem to be using a question mark to represent pi… You can do it instead by using symbol font: If you type “[symbol]p[/symbol]” you’ll get “[symbol]p[/symbol]”
As to your question, it does depend on the context. Usually, when you see a number expressed exactly (like [symbol]p[/symbol][sup]2[/sup]) in a technical science, it was derived mathematically, not experimentally. However, that mathematical derivation may be based on some physical assumptions. For instance, the exponent in the Law of Gravitation is exactly two, if the graviton is massless, and there are three spatial dimensions. People still see if they can determine the exponent experimentally, though, to see if it’s really two. What they’re actually determining is whether those two assumptions are valid.
A “parameter” is usually taken to mean something which can be varied, but I’m not sure if that’s a requirement. In any event, even if it is mislabelled, that won’t change any of the real physics involved. What we call things really doesn’t matter, just how we use them.
So you have a mysterious equation which uses the term capital-pi, and it’s squared, and you can’t talk about it, but ask us why it’s so?
The symbol capital-pi (I don’t know how to make it in VBcode) is used as far as I know exclusively to indicate the multiplication of a series. I can’t think of any times you might want to square this.
If you want anyone here to have a clue what you’re talking about, you need to ask your question with some more details.
Thank you, Chronos; I was truly trying to differentiate the use of big-pi and little-pi, but but I used the HTML codes rather than the much superior vB symbol font. The HTML version looks OK on my browser, though.
My questions concerned “[symbol]P[/symbol]²” rather than “[symbol]p[/symbol]²”. If there are still people trying to verify the exponent in the basement of the Gravity Law, then you have answered much of my question, Chronos.
Sorry to be enigmatic, CurtC. When I started this thread, everything seemed straightforward to me: I noticed no mystery in the term “[symbol]P[/symbol]²”. As the thread progressed and I felt that it would be imprudent of me to mention the context, I began to regret starting it.
Nonetheless, CurtC, if even one person reads this thread who understands the context, I shall be more than satisfied that I have not wasted my, nor you-all-un’s, time; even if such a hypothetical person doesn’t, or can’t, respond.
Yes, I’ve thought about this, but space would have to be a different shape to accomodate this (maybe if it was arranged so that a right angle wasn’t 90[sup]o[/sup], or the ‘rubber sheet’ was actually a ‘rubber dish’ - I’m not talking about curvature, or rather I am, but at a lower level).
Chronos: If you see the capital Pi as a question mark, you are probably using an out-of-date browser, one which doesn’t support Unicode. May I suggest upgrading?
Parameter Π²: In order for us to answer your question, you have to specify what you mean by Π; the answer will be different in different contexts. For instance, in the equation:
F = GMm / R[sup]2[/sup]
R is a variable, representing the distance. However, in the equation:
R is a constant, the Rydberg constant. If there were one most-popularly accepted meaning for the letter Π (like there is for [symbol]p[/symbol], or pi) we would know what you’re talking about. But just like R, there isn’t.
While that is the definition of pi, there is nothing implicit in that definition that says that pi is constant.
The OP, I believe, is not talking about pi. The OP wants to know about some other quantity called Pi. (Note that it’s capitalized.) Just what Pi is, though, is classified.
I’m familiar with the Pi+, Pi-, and Pi 0 mesons (those should all be a capital Pi followed by a superscript symbol, but I don’t know what I’m doing), but not Pi ². I assume you aren’t referring to Pi(x), the number of primes less than or equal to x.
All for the best, though, I suspect. Sorry for the ambiguity; but thanks for the welcome!