31–39 of 39 posts
Earlier quoted context omitted.
Proof for the curious: http://www.google.com/search?q=number+of+seconds+in+a+year+d...
I understand what you did, but the mathematician in me cringed at the word "proof" in that comment.
Hmm, whilst it's true physicists often simplify equations to really understand the problem, I can't think of a variable in quantum mechanics we "don't know to within 2 orders of magnitude". Especially one called alpha, which usually denotes the fine structure constant, which we know to better than 1 in a billion... Anyone have some thoughts on what it could be, if true? http://en.wikipedia.org/wiki/Fine-structure_con…
However, when would you use the pi = 3 approximation? Certainly not when you're in front of a computer, or if you were preparing some experimental results for publication. But, if you're in the lab and need to quickly make some calculations, or just to see if something is feasible and worth spending more time on, pi = 3 isn't so bad.
Example, measuring the fine structure. Sure, you can predict where these energy levels are supposed to be to probably whatever our error on knowing the mass of an electron is. And because you know the fine structure so precisely, you should be able to make a very accurate prediction on where that is. However, throw most of those digits out the door, because a lot will be hidden behind doppler broadening. So when you make your measurement in your fabry perot etalon, you'll probably make a precise measurement
http://en.wikipedia.org/wiki/File:Fabry_Perot_Etalon_Rings_F...
but how accurately can you really measure the position of those fringes? Sure, free spectral range probably lets you get down to about MHz region or so, but the doppler broadened linewidth is probably an order larger than that. Which brings us back to, you've got these experimental errors, why care about 9 digits of precision if you just want a quick and dirty calculation to get things set up?
Anyways, that's all he's trying to say. In most experiments, there will be some sort of experimental error hurting you. Be sloppy in the beginning just to get a feel for things.
I will never forget an high school assignment in physics in France, where we were asked to calculate how a wheel of a given diameters would put marks to the road if it had a pen attached at a given position. Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. So I started by "let's define pi=3" I got a bad grade on that one, even after I protest…
>Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. In English, calculus and calculation are two different things. And there are a number of grammatical errors in that sentence that make the meaning unclear. I'm noting this because if the teacher allowed you to do simpler calculus so long as you maintained an error margin of 10%, that's differe…
Earlier quoted context omitted.
Proof for the curious: http://www.google.com/search?q=number+of+seconds+in+a+year+d...
I understand what you did, but the mathematician in me cringed at the word "proof" in that comment.
How was it funny? It seems like a sound reasoning, depending on whatever alpha represents.
He basically Nerd-burned them, and that is something I can get behind.
Pi ~ 3, but we also often need Pi^2, which is better approximated as 10. (I actually got into an argument about rounding Pi^2 to 10 once with a person who liked to round Pi to 3 ...)
(It's too bad that the combination Pi^2 + Pi occurs basically never.)
Off topic, but why is the "pi" character in most common fonts so poorly designed? It always seems to have a straight line at the top rather than a tilde-like stroke and it confuses me just about every time.
I had the same problem, I thought the author mistakenly used ∏ but I see in my browser tab that it's correctly lowercase.
Earlier quoted context omitted.
>Our teacher always said she accepted all result with an error of less than 10% if we did that by making the calculus easier. In English, calculus and calculation are two different things. And there are a number of grammatical errors in that sentence that make the meaning unclear. I'm noting this because if the teacher allowed you to do simpler calculus so long as you maintained an error margin of 10%, that's differe…
Newton's calculus is just one example of a calculus. A calculus is any set of mechanical rules for manipulating mathematical symbols. Calculation is the process of applying those rules. Cf. the lambda calculus. The branch of mathematics involving limits, functions, derivatives, and integrals is analysis.
Everywhere I've studied, it's been referred to as simply calculus. Wikipedia says the same. I did take a class called analysis of functions in high school as an advanced track pre-calculus, but your definition really does not apply in the States at any rate. Where did you hear Analysis used to specifically apply to what we call calculus in the States?
Earlier quoted context omitted.
Newton's calculus is just one example of a calculus. A calculus is any set of mechanical rules for manipulating mathematical symbols. Calculation is the process of applying those rules. Cf. the lambda calculus. The branch of mathematics involving limits, functions, derivatives, and integrals is analysis.
>The branch of mathematics involving limits, functions, derivatives, and integrals is analysis. Everywhere I've studied, it's been referred to as simply calculus. Wikipedia says the same. I did take a class called analysis of functions in high school as an advanced track pre-calculus, but your definition really does not apply in the States at any rate. Where did you hear Analysis used to specifically apply to what we…
