ouin wrote:They disassembled it and re-assemble it I guess.

With the extra-part, they've made the second one..

You mean it's...

Banach-Baby?

- Fri Dec 11, 2009 10:05 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0674: "Natural Parenting"
- Replies:
**100** - Views:
**23702**

ouin wrote:They disassembled it and re-assemble it I guess.

With the extra-part, they've made the second one..

You mean it's...

Banach-Baby?

- Sun May 31, 2009 8:17 pm UTC
- Forum: Science
- Topic: Comical mistakes in your homework.
- Replies:
**144** - Views:
**17276**

In an optimisation problem, I was to calculate the most energy-efficient way to drive a car up a hill in a fixed amount of time. I forgot to add the constraint to the Lagrangian and ended up with that the optimal solution was to let the car roll down the hill...

- Sun May 31, 2009 8:12 pm UTC
- Forum: Mathematics
- Topic: Why does the Limit of Sin(x)/x as x approaches 0 equal 1?
- Replies:
**37** - Views:
**11922**

Using L'hôpital's rule to prove this limit is one of my pet peeves. When you use L'hôpital's rule, you derive \sin x to get \cos x . But how do you know that? \frac {\rm{d}}{\rm{d}x} \sin x = \lim_{h \rightarrow 0} \frac {\sin (x+h)-\sin x}{h} = \lim_{h \rightarrow 0} \frac{ \sin x (\cos...

- Thu Mar 19, 2009 10:04 pm UTC
- Forum: Mathematics
- Topic: Nice graphs?
- Replies:
**19** - Views:
**6200**

But... how?

- Thu Mar 19, 2009 6:23 pm UTC
- Forum: Mathematics
- Topic: Reverse Gravity
- Replies:
**8** - Views:
**1396**

Mathmagic wrote:Or it's that everything has a center of mass, and you can treat the object as if all the mass was concentrated in a point mass at that point.

If you're close to the object, you can only do that if the object is spherical.

- Wed Mar 18, 2009 8:49 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0557: "Students"
- Replies:
**223** - Views:
**67417**

A first for me: Get the fuck out of my head Randall! I had pretty much exactly this dream this morning. Except that I figured out, during the dream, that I was in the clear, since I wasn't taking that class anyway. Also, I'm still on my master's degree. On second thought, this might not be Randall b...

- Wed Mar 11, 2009 8:07 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0179: "E to the Pi times I"
- Replies:
**161** - Views:
**54655**

...which, I'm sure you'll agree, is quite clumsy and inelegant tell me why you'd want to define i = \sqrt{-1} Not very clumsy. The equality holds up to a sign change anyway. But there is an inelegancy in the inability to extend it to other powers of complex numbers. I don't want to define i as \sqr...

- Tue Mar 10, 2009 8:12 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0179: "E to the Pi times I"
- Replies:
**161** - Views:
**54655**

Or you could just say that

[math]\sqrt{ab} = \sqrt{a} \sqrt{b}[/math] is not a general identity, but only holds when at least one of a and b is real and non-negative.

Extending the domain of a function often means giving up some structure.

[math]\sqrt{ab} = \sqrt{a} \sqrt{b}[/math] is not a general identity, but only holds when at least one of a and b is real and non-negative.

Extending the domain of a function often means giving up some structure.

- Sat Mar 07, 2009 2:31 pm UTC
- Forum: Mathematics
- Topic: Tips on handwriting maths?
- Replies:
**21** - Views:
**3075**

For rho, I write something between [imath]\rho[/imath] and [imath]\varrho[/imath]. Slightly left-leaning and curving to the right at the bottom. Looks quite similar to a inverted 9, but dips below the line. I rarely confuse it with p.

[imath]\{[/imath] and [imath]\xi[/imath] might be my most similar glyphs, actually, especially if I'm sloppy.

[imath]\{[/imath] and [imath]\xi[/imath] might be my most similar glyphs, actually, especially if I'm sloppy.

- Sat Feb 28, 2009 1:06 pm UTC
- Forum: Mathematics
- Topic: Favorite math jokes
- Replies:
**1452** - Views:
**488693**

I don't get it. All natural numbers are tits?

- Sun Feb 08, 2009 6:10 pm UTC
- Forum: Serious Business
- Topic: Age Disparity Between Rights and Responsibilities
- Replies:
**22** - Views:
**2486**

I don't think there are any good ways to measure maturity. Age limits are obviously arbitrary, but they have the advantage that they cannot be (secretly) manipulated by the current government/other interest groups. For voting age, an alternative would be some kind of suffrage exam, which you would h...

- Tue Dec 30, 2008 3:58 am UTC
- Forum: School
- Topic: Awesome Teacher Quotes
- Replies:
**1764** - Views:
**399524**

An oldie I suddenly remembered for some reason: One day, the Science class had covered blood types, and had tested the blood type of some of the students. The teacher had also talked about how the blood types are inherited. The next day: Girl: Teacher, what you taught us yesterday was wrong. I asked...

- Wed Dec 17, 2008 3:45 pm UTC
- Forum: General
- Topic: Signed, Summer Glau
- Replies:
**48** - Views:
**19772**

At large, very good Summer Glau-ing, Dori. However: Claim 4: Obama is against Bush; V is against a president inspired by Bush. It remains unknown whether or not Chancellor Sutler was inspired by Bush. I am inclined to disagree with your claim. Granted, Obama is in opposition to Bush. However, Adam S...

- Wed Dec 17, 2008 1:10 pm UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

I shouldn't do this but... So we have got images of a pencil in a glass of water. Looking from some angles, the pencil appear to be bent, from others not. Through the curved glass, the pencil even looks thicker. All of these effects are explained by Snell's law. You claim todays physics can't explai...

- Tue Dec 16, 2008 7:18 pm UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

There is an object and there is an observer. How is the information about the object being communicated to the observer? Through light coming from a lightsource reflecting of the object (or generated by the object itself) and then reaching the observer. Note however, that the light being reflected ...

- Tue Dec 16, 2008 5:18 pm UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

I do not know how to make a drawing hree but it is simple - an object is placed in front of the mirror and u place a screen (I used a newspaper) that is higher than the object and extends beyond object even sideways (as suggested in the experiment) and u view the object from the top of the mirror a...

- Tue Dec 16, 2008 1:32 pm UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

The questions here were directed at Gammashield, but it seems to me that me and gamma are on the same side here, so: Photons don't come with little labels saying "I'm from the sun!". ....Photons don't come with little labels saying "I'm from the sun!". Photons fly out of the sun,...

- Mon Dec 15, 2008 8:10 pm UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

Another way to Gelsamels point: It isn't necessary that things are either wave or particle, the correct statement is "light is neither a wave nor a particle". What is it? To the best of our knowledge a linear state in a hilbertspace upon which operators that in certain regimes mirror part...

- Mon Dec 15, 2008 12:32 am UTC
- Forum: Science
- Topic: Dual nature of light, my mind is melting
- Replies:
**59** - Views:
**6890**

When we peep through the holes one by one, we find virtually no difference in the views from both the slits except that we cannot see light source from the slits in the dark band . (Emphasis mine.) Well... yeah. No light from the lightsource reaches the dark bands. Virtually no difference, except t...

- Sun Dec 14, 2008 11:31 pm UTC
- Forum: Science
- Topic: Downwind faster than the wind
- Replies:
**262** - Views:
**32666**

The threadmill might be the easiest way to show how it works. Assume that we tie the car to the frame of the threadmill, and let the threadmill drive the wheel, which again drives the propeller. Now what do we have? A rather strange electric fan. No violation of physics here. Now, this fan pushes a...

- Sun Dec 14, 2008 10:35 pm UTC
- Forum: Science
- Topic: Downwind faster than the wind
- Replies:
**262** - Views:
**32666**

Actually, I think this is possible. (And for the record, I've studied physics, if that gives me any authority.) The threadmill might be the easiest way to show how it works. Assume that we tie the car to the frame of the threadmill, and let the threadmill drive the wheel, which again drives the prop...

- Mon Dec 08, 2008 6:09 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0514: "Simultaneous"
- Replies:
**144** - Views:
**29268**

SocialSceneRepairman wrote:seladore wrote:I think they are both SR jokes. The twin paradox comes from SR, not GR.

As I recall, the paradox comes from special relativity, but the resolution comes from general relativity...

To be precise, the paradox comes from an invalid application of special relativity.

Also: great comic.

- Wed Dec 03, 2008 12:32 am UTC
- Forum: Mathematics
- Topic: Prime Number Proof
- Replies:
**24** - Views:
**2906**

Erathostenes' sieve is pretty good at finding primes in the range 1 to n.

- Mon Nov 24, 2008 9:45 pm UTC
- Forum: School
- Topic: What should I do with my life?
- Replies:
**7** - Views:
**1606**

You say you like genetic algorithms and writing in-browser games. How do you feel about programming in general? One possibility is going to a CS grad school. With some luck, you'll be able to do some research on genetic algorithms, and maybe work on more advanced games than in-browser. If you get in...

- Tue Nov 18, 2008 1:26 pm UTC
- Forum: Mathematics
- Topic: Alternating sum of product of binomial coefficients
- Replies:
**2** - Views:
**1581**

Thanks. Using generalized binomial coefficients and Vandermonde's identity did the trick.

- Mon Nov 17, 2008 2:44 pm UTC
- Forum: Mathematics
- Topic: Alternating sum of product of binomial coefficients
- Replies:
**2** - Views:
**1581**

In a numerics project, I've encountered the apparent identity \sum_{i=0}^k (-1)^i {2s-i \choose s-i} {k \choose i} = {2s-k \choose s} where (0 \leq k \leq s) . possibly with the generalization \sum_{i=0}^k (-1)^i {n-i \choose m-i} {k \choose i} = {n-k \choose m} Does anyone k...

- Sat Oct 04, 2008 8:00 am UTC
- Forum: Mathematics
- Topic: Arc of an ellipse
- Replies:
**10** - Views:
**1781**

What exactly do you want to achieve with this simulation? If you just want to see the orbits, there are several of implementations of orbit simulation freely available on the internet. For writing a implementation, that gives realistic results in a reasonable amount of time, you would have to use so...

- Mon Aug 11, 2008 4:48 pm UTC
- Forum: Mathematics
- Topic: Something I've been wondering since 7th grade
- Replies:
**22** - Views:
**4521**

There's a case to be made that multiplication is not repeated addition. (http://www.maa.org/devlin/devlin_06_08.html). I'm honestly not sure what to make of it yet, but the point he makes is that just because you come up with the same result multiplying and adding doesn't mean that you did the same...

- Fri Jul 04, 2008 6:29 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0445: "I Am Not Good with Boomerangs"
- Replies:
**132** - Views:
**41269**

This guy has mad boomerang skills:

- Wed May 21, 2008 4:31 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0426: "Geohashing"
- Replies:
**224** - Views:
**39548**

Call me crazy but I don't like the algorithms dependence on the stock market (not geeky enough for me I guess) What I'd propose is something like using the date and time possibly concatenated with the least significant longitude and latitude coordinates as the input to the hashing algorithm which s...

- Mon May 19, 2008 8:45 pm UTC
- Forum: Science
- Topic: How many ways can you empty a glass of water?
- Replies:
**129** - Views:
**12896**

As far as I can see, no one has said this, so:

siphon it out.

make the water superfluid. (Yeah, I know this isn't possible)

siphon it out.

make the water superfluid. (Yeah, I know this isn't possible)

- Sat May 10, 2008 7:50 am UTC
- Forum: Science
- Topic: Bizarre facts
- Replies:
**234** - Views:
**44867**

George Paget Thomson, who received the Nobel prize in physics in 1937 for proving the electron has wave properties, was the son of Joseph John Thomson, who received the Nobel prize in physics in 1906 for proving the electron has particle properties.

- Mon Apr 28, 2008 9:05 pm UTC
- Forum: Science
- Topic: calculating Sols Orbit
- Replies:
**14** - Views:
**1302**

Assuming there are no external forces on the solar system, total momentum is conserved. Choosing the simplest reference system - that is, the one which follows the solar system's center of mass - you can set \sum \vec{p} =0 Since you know every planet's mass and initial velocity, and the sun's mass,...

- Fri Apr 25, 2008 3:21 pm UTC
- Forum: Mathematics
- Topic: "Mathematics is a young man's game"
- Replies:
**12** - Views:
**3535**

Still, Euler, Gauss, Hilbert and Erdös all showed excellence early. It appears that if you haven't done anything MONUMENTAL before the age of 30, you never will. 1) But so what? If mathematics is what you love, and you're good at it, you should pursue a career in it. Will you have a theorem name...

- Mon Apr 21, 2008 4:12 pm UTC
- Forum: Science
- Topic: LHC Dangerous?
- Replies:
**372** - Views:
**88092**

I was wondering, exactly how dead on will the particle collisions at LHC be? I did some quick, back-of-the-envelope calculations, and found out that even if there exists mBH at the relevant energies (and they are created), and even if Hawking radiation doesn't exist, mBH's can't be captured by the e...

- Mon Apr 14, 2008 6:22 pm UTC
- Forum: Mathematics
- Topic: Interesting examples
- Replies:
**13** - Views:
**2144**

If you allow the function to have power series that does not converge to it, the example is less pathological, but still rather weird. Let g(x)=\begin{cases}e^{-\frac{1}{x^2}}&\text{if }x\neq 0,\\ 0&\text{if }x=0,\end{cases} and let \{q_n\}_{n=1}^\infty be an enumeration of the ratio...

- Mon Apr 14, 2008 3:07 pm UTC
- Forum: School
- Topic: Awesome Teacher Quotes
- Replies:
**1764** - Views:
**399524**

This one is from my fluid mechanics prof last fall. We were covering gravity waves. "So, in shallow water, for example the Pacific, d = 4000 m" (He then introduced a tsunami-size wavelength (I think 80 km), and since the important parameter is d/\lambda , 4000 m is actually "shallow w...

- Mon Apr 14, 2008 8:48 am UTC
- Forum: Mathematics
- Topic: Interesting examples
- Replies:
**13** - Views:
**2144**

There are a bunch of interesting stuff in Counterexamples in Analysis. I don't have it with me right now, but I'll post a few examples in the evening. The only ones I can think of off* the top of my head are basic examples, like the weierstrass function and the function that's nowhere continuous, bu...

- Mon Apr 14, 2008 8:38 am UTC
- Forum: Mathematics
- Topic: A cool thing about polynomials and squared roots
- Replies:
**6** - Views:
**1878**

A hint: We have [imath]\TeX[/imath] support now.

- Thu Apr 10, 2008 9:27 pm UTC
- Forum: Forum Games
- Topic: Ruin a Joke
- Replies:
**800** - Views:
**61113**

... where he meets the ex-husband of his former client, who has had a drink or three too many. The ex-husband recognizes the lawyer, which, in his eyes, is to blame for his agony. The ex-husband breaks his bottle and charges the lawyer. Luckily, the lawyer manages to avoid the drunken charge. The bo...