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1500 questions
85
votes
4 answers
Why did my friend lose all his money?
Not sure if this is a question for math.se or stats.se, but here we go: Our MUD (Multi-User-Dungeon, a sort of textbased world of warcraft) has a casino where players can play a simple roulette. My friend has devised this algorithm, which he himself…
Konerak
- 1,083
85
votes
6 answers
How to show that the commutator subgroup is a normal subgroup
It is suggested as an exercise in Serge Lang's book "Algebra" to show that the commutator subgroup $G^c$ of a group $G$ is a normal subgroup. I'd like to do that but I am afraid I need help, I think the first thing I need to figure out is how a…
harlekin
- 9,050
85
votes
19 answers
How to find perpendicular vector to another vector?
How do I find a vector perpendicular to a vector like this: $$3\mathbf{i}+4\mathbf{j}-2\mathbf{k}?$$ Could anyone explain this to me, please? I have a solution to this when I have $3\mathbf{i}+4\mathbf{j}$, but could not solve if I have $3$…
niko
- 977
85
votes
21 answers
How to generate a random number between 1 and 10 with a six-sided die?
Just for fun, I am trying to find a good method to generate a random number between 1 and 10 (uniformly) with an unbiased six-sided die. I found a way, but it may requires a lot of steps before getting the number, so I was wondering if there are…
P.A.
- 859
85
votes
0 answers
Regular way to fill a $1\times1$ square with $\frac{1}{n}\times\frac{1}{n+1}$ rectangles?
The series $$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}=1$$ suggests it might be possible to tile a $1\times1$ square with nonrepeated rectangles of the form $\frac{1}{n}\times\frac{1}{n+1}$. Is there a known regular way to do this? Just playing and not…
2'5 9'2
- 57,884
85
votes
2 answers
What is the proper way to study (more advanced) math?
Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think that I'm being lazy, I'm not thinking things…
anonymous
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84
votes
10 answers
Why does being holomorphic imply so much about a function?
I haven't yet started my complex analysis course (soon!), but recently (inspired by you guys) I've been looking into holomorphic functions. And wow, they're cool! There's so much stuff that's true about them... But my question is: why is being…
ShakesBeer
- 3,719
84
votes
4 answers
Why the emphasis on Projective Space in Algebraic Geometry?
I have no doubt this is a basic question. However, I am working through Miranda's book on Riemann surfaces and algebraic curves, and it has yet to be addressed. Why does Miranda (and from what little I've seen, algebraic geometers in general) place…
Potato
- 41,689
84
votes
6 answers
What's so "natural" about the base of natural logarithms?
There are so many available bases. Why is the strange number $e$ preferred over all else? Of course one could integrate $\frac{1}x$ and see this. But is there more to the story?
user218
84
votes
7 answers
Hanging a picture on the wall using two nails in such a way that removing any nail makes the picture fall down
A friend of mine told me that it's possible to hang a picture on the wall from a string using two nails in such a way that removing either of the two nails will make both the string and picture fall down. My friend also told me that I need to be…
Anonymous - a group
- 1,529
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84
votes
21 answers
Can someone explain to me how a formula for the sine function is derived?
I'm 14 years old, and I'm taking a geometry course over the summer to get ahead in school. We've reached a unit on right triangles and trigonometry. I have knowledge of mathematics up to Algebra 1, and have done some of my own explorations regarding…
some kid trying her best
- 1,185
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84
votes
5 answers
Math behind rotation in MS Paint
For those who don't know, MS Paint only has the options to rotate an image by right angles. To carry out an arbitrary rotation ($\theta^\circ$), the following hack is suggested : Horizontal skew by $\theta$ Vertical Stretch by $\displaystyle…
kuch nahi
- 6,897
84
votes
8 answers
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
If $f(x)$ is a continuous function on $(-\infty, +\infty)$ and $\int_{-\infty}^{+\infty} f(x) \, dx$ exists. How can I prove that $$\int_{-\infty}^{+\infty} f(x) \, dx = \int_{-\infty}^{+\infty} f\left( x - \frac{1}{x} \right) \, dx\text{ ?}$$
Hung Nguyen
- 1,881
84
votes
5 answers
(Theoretical) Multivariable Calculus Textbooks
(Note that I have used bold text frequently simply to highlight the key points of my question for those who do not have the time to read through it thoroughly (it is not very long, however); I hope this is not considered offensive.) There are many…
Amitesh Datta
- 21,549
84
votes
2 answers
What does the mysterious constant marked by C on a slide rule indicate?
Years ago, before everyone (or anyone) had electronic calculators, I had a pocket slide rule which I used in secondary school until the first TI-30 cane out. Recently I dug it out. Here's a photo of one end of it. As you can see, there's a number…
timtfj
- 3,062