4,020 reputation
1023
bio website
location
age
visits member for 3 years, 3 months
seen 19 hours ago

Oct
7
comment Matrix Algebra Question (Linear Algebra)
I think you're missing dfeuer's point. If you equate $A_{1,1}^3$ to $2A_{1,1}$ you get $-4 + 2(2-a) = -4$, which has one solution. Then it's just a case of checking it against the other three cells.
Oct
7
comment Filling 4l, 5l bottles from two 10l bottles
I think there is some ambiguity here as to what the desired outcome is. Does "take 2 litres of water each" imply that the water from the two big bottles shouldn't be mixed? Or is all of the water interchangeable, such that this should be understood only as saying that the big bottles should finish each containing 8 litres?
Oct
7
comment What is the upper bound on the error of a matrix multiplication
What have you tried? Where do you get stuck?
Oct
4
comment Logarithms and big O notation
Technically $O$-notation is used for upper bounds without any guarantee of tightness, so you could answer $O(n)$ to both questions.
Oct
3
comment How can I convert an axis-angle representation to a Euler angle representation
The key terms I think you're missing are axis-angle and Euler angle representations. There doesn't seem to be an existing question about the conversion from axis-angle to Euler angles, but knowing the terminology is a good starting point when searching.
Oct
3
comment An Olympiad Problem (tiling a rectangle with the L-tetromino)
What have you tried? Where do your ideas fail?
Oct
1
comment Solving intersection of 4 quadratic equation with constraints
It might be a useful perspective to post-multiply both sides of your equation by $Q$ and get $Q\bigotimes P = R \bigotimes Q$.
Sep
26
comment Find the result of a weird looking sum
For a given $x$, how many $i \in \mathbb N$ are there such that $\lfloor\sqrt i\rfloor = x$?
Sep
25
comment How to put $N$ elements in $M$ cells separated by a distance $D$
You may find it helpful to ditch the "of course" constraint and make the answer 0 in that case. This allows you to write a recurrence...
Sep
17
comment Proof for solar declination angle?
Hmm, maybe not quite as simple as I thought.
Sep
17
comment Proof for solar declination angle?
@Sri, there's probably a more elegant geometric approach, but I'm not a geometer and I attack geometry problems by brute force. Although now that I think about it, if you're familiar with spherical geometry then by simply assuming that $|B| = |C|$ you can reduce it to a simple spherical triangle problem.
Sep
17
comment History of the theory of equations: John Colson
On a quick skim I don't spot the roots of unity, but I do spot some geometrical diagrams. Can you give some page references in the PDF you link to the particular points of interest?
Sep
16
comment Proving a formula about binomial coefficients
Have you tried Gosper's algorithm?
Sep
16
comment Kaprekar's constant-related problem
(And that includes the extraneous fixpoint $a=b=c=d$ -> $0000$)
Sep
13
comment How to this calculate summation formula more quickly
There must be some way to structure it as a loop over the gcd.
Sep
13
comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number
Or to put it in simpler terms: every practical number greater than $1$ is even and hence equivalent to $0$, $2$, or $4\pmod 6$. But polygonal numbers with $n=3$ enumerate all multiples of $3$ greater than $3$, so in particular all practical numbers which are equivalent to $0\pmod 6$; and polygonal numbers with $n=4$ enumerate the equivalence class of $4\pmod 6$ starting at $10$. That just leaves the practical numbers equivalent to $2\pmod 6$, and since they're multiples of $2$ half their value is equivalent to $4\pmod 6$.
Sep
13
comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number
I might consider putting up a list somewhere else, but I don't think that OEIS tends to go in for excessively long lists. In the meantime, here's some code (I've optimised it and ported it to Java, which has a priority queue in the core library).
Sep
12
comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number
There is a quick method to enumerate them but it uses a bit of memory. From the Stewart/Sierpinski characterisation we can generate them using a priority queue; for efficiency, store tuples $(n,p,\sigma(n),p^{a+1})$ where $p$ is the largest prime factor of $n$ and $a$ is its multiplicity in $n$. Initially insert $(1,2,1,2)$. When you pop a tuple, push $(np,p,\sigma(n)(p^{a+2}-1)/(p^{a+1}-1),p^{a+2})$ and $(nq,q,\sigma(n)(q+1),q^2)$ for all prime $p<q\le 1+sigma(n)$. I've implemented this in C# and get up to 30000 in 13 seconds. By not pushing tuples with $n>30000$ it takes 0.04 seconds.
Sep
11
comment Defining bijective function $f:\mathbb{N}\times\mathbb N\to\mathbb N$
Can you not compose the function you know for $\mathbb N \cup{0}\times \mathbb N \cup{0}$ with a bijection from $\mathbb N$ to $\mathbb N \cup{0}$?
Aug
30
comment Which of the following matrices are non singular?
possible duplicate of Singular or non-singular matrices