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16h
comment In how many ways can $1000000$ be expressed as a product of five distinct positive integers?
It might be worth explaining how this ensures distinctness; it's correct, but it took me a minute to see why. Still, this is definitely a straightforward way.
1d
comment Show that A*B and B*A have the same order
This has to be a real candidate for 'most duplicated question on the site'.
1d
comment Forming a (1,1)-tensor field from a (0,2)- and (2,0)-tensor field
You're trying to go in a coordinate-dependent fashion, but a tensor is not a coordinate-dependent thing! You need to prove that C is a tensor; that is, that it transforms appropriately under changes of coordinates.
1d
comment Technique for proving four points to be concyclic
Maybe I'm dense, but why are opposite angles adding up to 180 degrees? And for that matter, what are 'opposite' angles in this context? We don't know that any two of these points are forming a diameter...
2d
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2d
comment can I draw a 2nd degree 2 dimensional surface trough 3x3 points, like I can draw a 2nd degree polynomial through any 3 points
A simpler version of this occurs one degree down: $2$ points determine a line, but $2\times2$ points overdetermine a plane; they can only be bilinearly interpolated through, and that surface is a (ruled) quadric.
2d
awarded  Nice Answer
2d
comment What is this pattern called?
@AlexMcKenzie Also, congratulations on finding this! This sort of pattern-hunting is an excellent way of experimenting in mathematics and learning about all sorts of facets of its vast world.
2d
comment What is this pattern called?
@AlexMcKenzie That's essentially correct - and because multiplication is a fairly smooth function, you don't 'skip' multiples of $n$ as you multiply out successive numbers, so your band coloring mod $n$ essentially guarantees that you'll draw out hyperbolic arcs along each multiple of $n$.
2d
revised What is this pattern called?
Fleshed things out a bit more.
2d
comment What is this pattern called?
@AlexMcKenzie In fact, let me flesh out my answer a little bit to explain what I mean by that first sentence...
2d
comment What is this pattern called?
@AlexMcKenzie The last-digits multiplication that you're talking about is exactly modular arithmetic (specifically, it's the multiplication table mod $n$). A cute example: look at the table of last digits for the base-7 multiplication table. Notice that every row has each non-zero number exactly once, and (by symmetry) so does every column? This isn't a coincidence! This will happen whenever your base is a prime; the numbers mod $p$ form what's called a group under multiplication.
2d
revised What is this pattern called?
added 232 characters in body
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answered What is this pattern called?
Apr
25
comment To add the following pair of combinatorials
The sum isn't always a (non-trivial) binomial. E.g., take $N=8$ and $y=3$; then the sum is ${7\choose 3}+{6\choose 2}$ $=35+15$ $=50$, and the latter only appears as $50\choose 1$. Are you sure you've written things down correctly?
Apr
25
comment Isn't the axiom of determinacy inconsistent with ZF? What am I overlooking?
One obvious problem with your argument: there's nothing specific to AD about it. If it were correct, you could show that ZF$\implies$ ZFC, which of course is known to not be true. But more specifically: just because there's a model of a theory $T$ in ZFC doesn't mean that the model (internally) satisfies choice. A choice function may exist for sets in the model but not be part of the model itself.
Apr
25
comment Work back from atan2 please?
@hazhazzz What you're seeing is exactly the degrees-to-radians issue. In fact, you're almost certainly best off never storing degrees at all; if you need to show them to a user then that's one thing, but if you're only going back and forth between angles and their associated vectors, then you almost certainly just want to store angles in radians. (Or never store angles at all and only store vectors, but that's another matter entirely...)
Apr
25
comment Work back from atan2 please?
You can't derive them precisely (because, for instance, your axes could have been 0.5 and 0.5 as easily as 1.0 and 1.0); but up to that scaling factor, the two inputs are simply $\sin(\theta)$ and $\cos(\theta)$, where $\theta$ is the angle that atan2() returns you.
Apr
24
comment How to solve $x^3\equiv 10 \pmod{990}$?
Note that the second one is $-1\bmod 11$, too.
Apr
24
comment Sum of odd Fibonacci Numbers
There's a straightforward proof by induction. Suppose that it's true for a given $n$ - i.e., that $F_{2n}=\sum_{i=1}^nF_{2i-1}$; then $\sum_{i=1}^{n+1}F_{2i-1}=F_{2n+1}+\sum_{i=1}^nF_{2i-1}=F_{2n+1}+F_{2n}$...