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1500 questions
98
votes
4 answers
Finding the transform matrix from 4 projected points (with JavaScript)
I'm working on a project using Chrome - JS and WebKit 3D CSS3 transform matrix. The final goal is to create a tool for artistic projects using projectors and animation - somewhat far away from using maths...
I'm using a projector to project several…
mika
- 1,003
98
votes
1 answer
$4494410$ and friends
The number $4494410$ has the property that when converted to base $16$ it is $44944A_{16}$, then if the $A$ is expanded to $10$ in the string we get back the original number.
$3883544142410_{10}=3883544E24A_{16}$ is another.
These numbers are in…
Ross Millikan
- 374,822
98
votes
5 answers
Cover of "Gödel, Escher, Bach"
Consider the cover image of the book "Gödel, Escher, Bach", depicted below. The interesting feature is that it shows the existence of a subset of $\mathbb{R}^3$ which projects onto $\mathbb{R}^2$ in three different ways to form the letters of the…
98
votes
8 answers
Does mathematics become circular at the bottom? What is at the bottom of mathematics?
I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.
Now is the "=" taken…
user119615
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- 112
98
votes
7 answers
How can adding an infinite number of rationals yield an irrational number?
For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number.
E.O.
- 6,942
98
votes
16 answers
What's the difference between stochastic and random?
What's the difference between stochastic and random?
Red Banana
- 23,956
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- 192
97
votes
7 answers
A Case Against the "Math Gene"
I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the phrase "one is either a 'math person' or not". That…
Austin Mohr
- 25,662
97
votes
3 answers
What is "ultrafinitism" and why do people believe it?
I know there's something called "ultrafinitism" which is a very radical form of constructivism that I've heard said means people don't believe that really large integers actually exist. Could someone make this a little bit more precise? Are there…
Noah Snyder
- 10,005
97
votes
19 answers
Should I put number combinations like 1111111 onto my lottery ticket?
Suppose the winning combination consists of $7$ digits, each digit randomly ranging from $0$ to $9$. So the probability of $1111111$, $3141592$ and $8174249$ are the same. But $1111111$ seems (to me) far less likely to be the lucky number than…
arax
- 2,779
97
votes
7 answers
Density of sum of two independent uniform random variables on $[0,1]$
I am trying to understand an example from my textbook.
Let's say $Z = X + Y$, where $X$ and $Y$ are independent uniform random variables with range $[0,1]$. Then the PDF
is
$$f(z) = \begin{cases}
z & \text{for $0 < z < 1$} \\
2-z & \text{for $1 \le…
Zhulu
- 1,259
97
votes
10 answers
What is $\sqrt{i}$?
If $i=\sqrt{-1}$, is $\large\sqrt{i}$ imaginary?
Is it used or considered often in mathematics? How is it notated?
Gordon Gustafson
- 3,365
97
votes
6 answers
Is the notorious $n^2 + n + 41$ prime generator the last of its type?
The polynomial $n^2+n+41$ famously takes prime values for all $0\le n\lt 40$. I have read that this is closely related to the fact that 163 is a Heegner number, although I don't understand the argument, except that the discriminant of $n^2+n+41$ is…
MJD
- 65,394
- 39
- 298
- 580
97
votes
7 answers
97
votes
10 answers
Why is 'abuse of notation' tolerated?
I've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange. It seems to all be forgiven with a wave of the hand. Why do we tolerate it at all?
I understand if later on in…
Korgan Rivera
- 4,168
97
votes
3 answers
Can a limit of an integral be moved inside the integral?
After coming across this question: How to verify this limit, I have the following question:
When taking the limit of an integral, is it valid to move the limit inside the integral, providing the limit does not affect the limits of integration?
For…
Thomas Russell
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