Recent content by dodo

Post correction: I did assume that the ball's trajectory was not exactly vertical; an exact vertical trajectory represents a degenerate ellipse, which may explain the apparent puzzle of my hand being at two places on the paper. Let's continue assuming that the trajectory is a proper ellipse...

Hi, apologies if questions of the same form have been asked by laymen multiple times. (You must all be tired of this!) I tried to search on the forum, but I did not find my exact question answered. For context, I have some university math background, but when it comes to physics I am pretty much...

Perhaps there is no need for actual clocks. I wonder if you'd be able to make educated guesses about time slowing down, if all matter were closer to each other, as in the early universe. P.S.: By the way, thanks mgkii for the links, I'm barely starting to skim over them, but there's a lot of...

Hi all, I have a layman question, if I may. As you know better than I do, all sort of conclusions have been drawn from observations of the Doppler shift in light from distant objects: from the universe expansion, to the Big Bang, to the hypothesis of dark energy. My question is, has time...

Thanks for the advice, Wolfman, I'll give simpler 1-D models a look.

Hi, Chet, thanks for the input - I suspect I had in mind a scalar field all along and, when it comes to vector fields, I need to move back a few squares and review my vector calculus. Thanks again!

Apologies for the terribly misquoted equation at the end. I'm trying to edit the above post, but apparently I can't after a while. Please ignore the second half of the above post, from "A similar operation..." onwards. Also, a boldface is probably missing in the first equation. Doh! I got a...

Hi, I am doing an introductory course on fluid mechanics, and I'd like some intuition (that's why I'm posting on the engineering forums and not on the math forums, even if I'm studying for a degree in math) about the concept of the total derivative and, particularly, its convective component...

Hi, I think you may have answered your own question: if you are willing to accept that the RHS above can be rewritten as \prod_{j = 0}^{n - 1} ( x - a_j ) where a_j (with j=0,1,...,n-1) are the n-th roots of the complex number in polar form r e^{i \theta}, then your question can be rephrased...

Hi, vulpe, I'd attempt the swaps that put each peg in place. In your example, 5,2,1,4,6,3 1,2,5,4,6,3 (1,5) 1,2,3,4,6,5 (3,5) 1,2,3,4,5,6 (5,6) hence this one is odd. At worst, you'd do as many swaps as elements are (minus 1, actually).

Correct me if I'm wrong, but I believe 0≤x≤10 is not a region; 0<x<10 is. You may want to check the problem statement.

Is there a 'distance' function, a way to quantify how close or how similar two items are (so that you place similar items in the same set)? (Examples would be assigning customers to their closest service center, or grouping objects of similar colors.) If this sounds like the case, it may be a...

The Linear & Abstract Algebra forum had its description changed to include number theory, but in a somewhat hasty way. I wonder if it would be possible to change Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory. to Vector spaces and linear...

Is the Golden Ratio a requirement? If you were to use 1.7, or 1.6, or 1.5, or 2, how different would the figure be?

Be sure to activate your emotional chip, and scan singing to a tune. (Sorry. Couldn't help it.)