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Jun
27
comment Getting the max/min longitude/latitude within a distance from a point
@sandis, the best approach probably depends on your restrictions on d and plausible latitudes, but it's really a data structures question rather than a mathematical one. A relatively simple approach would be to use oct-trees; for more sophisticated approaches look at papers from the GIS community or search for terms like k-nearest.
Jun
14
comment Bat and ball calculations
Perhaps a more pertinent question is "Why would you work it out in MS Excel?"
Jun
7
comment Find the remainder when $ 12!^{14!} +1 $ is divided by $13$
Note that the original problem can also be solved by Fermat's little theorem: $12!^{12} \equiv 1 \pmod{13}$.
Jun
6
comment Finding a grammar for a formal language
Do you realise that this language is just [ab]*?
May
21
comment Change of coordinate system on a sphere
$L \times O$ is intended to be a cross product in the Euclidean embedding, i.e. one of the two poles of which $LO$ is (part of) the polar. The descriptions of $LP'$ and $PP'$ are intended to clarify what you mean by local lat and long. $LO$ and $NP$ cannot possibly be parallel, because on the surface of a sphere two lines are parallel only if they are collinear, and $N$ is not on $LO$ by construction.
May
21
comment Why do the Fibonacci numbers recycle these formulas?
Putting the last row into the OEIS search turns up some sequences with a few references. They would be a good place to start looking for an answer.
May
19
comment Change of coordinate system on a sphere
To clarify what you know: let $L$ be the local origin, $O$ be the true origin; $N$ be the "North Pole" of the local coordinate system (i.e. $L\times O$ normalised); let $P'$ be the intersection of $LO$ with $NP$; you know the lat and long of $L$ in the global system, the (signed) distance $LP'$= local longitude, and the (signed) distance $PP'$= local latitude?
May
15
comment Complex roots of $z^3 + \bar{z} = 0$
You only find 3 solutions, but you haven't explained why you're discarding two (x, y) pairs.
May
15
comment Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?
I don't get it. What's "English" about a temperature scale invented by a German who was born in Poland and lived in the Netherlands?
May
14
comment Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?
Celcius to English? What English temperature scales are there? Kelvin would be the closest (although he was Irish by birth and arguably Scottish by adopted), I suppose, but I don't think they teach absolute temperature at that age.
May
8
comment How to merge two poly Bézier curves?
If they were simple polygons, would you be able to do it? Can you find the intersection of two Bézier curves? Can you generate a Bézier curve which is a continuous subset of another Bézier curve?
May
2
comment In how many ways can a number be expressed as a sum of consecutive numbers?
An equivalent statement to that main result is given in the comments on A001227, although without reference.
May
1
comment Graph theory - A type of undirected simple finite graphs
What does the notation $\{a; b\}$ mean? Is that a two-element set, or an uninterrupted range of integers?
Apr
29
comment Intuition and derivation of the geometric mean
And as a point of interest, there are at least two other means which are $f^{-1}(\textrm{arithmetic mean}(f(x_i)))$, namely the harmonic mean ($f(x) = x^{-1}$) and the RMS ($f(x) = x^2$).
Apr
26
comment Why is the Connect Four gaming board 7x6? (or: algorithm for creating Connect $N$ board)
I recall one of the people who solved the game observing that 6x7 is the smallest board which isn't easily shown to be a draw.
Apr
18
comment A sum involving powers of binomial coefficients.
@hkju, see edit.
Apr
18
comment Are computers going to be able to discover and prove important mathematics theorems?
@JonasKibelbek, NP-hard, not NP-complete. There are certainly some theorems whose proof is exponentially larger than the theorem, so theorem proving isn't in NP.
Apr
17
comment A Curious Binomial Coefficient Sum
What do you consider to be a "simple function"? The theory behind Gosper's algorithm will tell you that if the sum exists as a hypergeometric then it's a rational polynomial times the summand.
Apr
16
comment Divide and conquer - Algorithm MYST
FWIW a trivial variant on this algorithm is stooge sort, and the question is equivalent to exercise 8-3 of Introduction to Algorithms by Cormen, Leiserson, and Rivest.
Apr
16
comment Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?
This can be made more symmetrical as $(1 - n\bmod 4)(1 - n \bmod 2)$