Recent content by Serious Max

Interestingly, Shankar (Yale) in his YouTube lectures actually derives it the other way around: assumes we know (as he derives in an earlier lecture) this kinematic formula and derives the formula for work. The kinematic formula was derived from combining other two. (10:30; can't link)

I guess that wouldn't hurt.

Yes, I assume that's because it's a very introductory book. But thank you for pointing it out, had to think for a bit about this one. Seems like you answered this yourself? Or is there something else? Step 3: A cylinder has ##V=2n##, ##E=2n+n=3n##, ##F=n##, hence ##V-E+F=0##. Basically each...

Ah, I think I got it. In proving ##V-E+F=2##, we first proved that if we removed one face from a polyhedron we could prove that ##V-E+F=1##, and then adding the removed face we'd get 2: ##V-E+F=1+1##. Then this result was shown to apply to a sphere, which is just an inflated polyhedron in this...

Yes, p is the number of holes, for sphere p=0, for torus p=1, for the shape they give p=2. But the problem I have is I don't understand what they do in the highlighted step to arrive at the formula. They go something like: 1) For a regular sphere ##V-E+F=2## 2) Now we have a sphere with ##2p##...

Could someone explain what's happening here with subtracting $2p$? Was thinking it could result from adding and/or subtracting edges of faces on the left-hand side but doesn't seem to work. This is from Courant's "What is Mathematics"

Just checking. I solved it incorrectly a couple times. And actually corrected it as I was posting it here, when I realized I made a mistake once again. SteamKing, right. That's better :).Thanks.

Homework Statement When you drop an object from a certain height, it takes time T to reach the ground with no air resistance. If you dropped it from three times that height, how long (in terms of T) would it take to reach the ground? Homework Equations ##x=x_0+v_{0x}t+\frac{1}{2}a_x t^2## The...

Here (at ~3:50) they say if the ship reaches 99% of the speed of light, a single day on the ship = year on Earth. But it looks like it's going to be one week on Earth. http://cosmology.com/images/3TimeDilationTable1.jpg Is it just a simplification of some sort in the video?

I re-edited my post a few times :) But you seem to have commented an earlier version.

So, as I understand, "If" expresses one of the many criteria for something to be done for certain (although, we don't know how many there are, it might be that this critertion is the only one, or maybe there are multiple). And "only if" merely gives restrictions, as to when something CAN be...

Used this http://en.wikipedia.org/wiki/If_and_only_if#Distinction_from_.22if.22_and_.22only_if.22

p water warm w water not cold q take a shower 1) p ## \rightarrow ## q 2) w ## \leftrightarrow ## q 3) p ## \leftarrow ## q ("if the water is not warm, then you will definitely not take a shower" = if I'm taking a shower, then you can be sure the water is warm, but that doesn't mean that if the...

Thanks. So should it be along the lines of: 1) water is warm => I take a shower 2) water is not cold (warm, cool etc) => I take a shower; otherwise, if the water is cold, I will not take a shower 3) water is warm => I might decide to take a shower; otherwise, if the water is not warm...

Three statements: 1) I will take a shower if the water is warm. 2) I will take a shower unless the water is cold. 3) I will not take a shower unless the water is warm. How different are their meanings? First guess was: 1) water is warm => I take a shower 2) water is not cold = water...