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Jul
4
comment Seeking formula for a custom game mechanic
Ross' answer gives the exact solution if you let the time step tend to 0. The advantage of using an exact solution is that you can vary your time step without affecting the results (modulo rounding errors on the order of a couple of ULP). However, if you want to complicate the equations by going to solid bodies, handling collisions, etc. then incremental calculation with fixed time step is likely to be more straightforward. There's a separate gamedev.stackexchange.com where you'll find plenty of questions and answers about building physics engines.
Jun
29
comment Does this ratio converge to the Golden Ratio?
It may be a useful observation (provable by induction) that each column becomes constant $(k-1)!$ after a triangular-number $k(k-1)/2$ of smaller values.
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
27
answered Getting the max/min longitude/latitude within a distance from a point
Jun
14
comment Bat and ball calculations
Perhaps a more pertinent question is "Why would you work it out in MS Excel?"
Jun
9
awarded  Civic Duty
Jun
8
awarded  Constituent
Jun
8
awarded  Caucus
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
28
answered graph-theory task
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
18
answered The game Officers
May
18
comment Cryptography puzzle
Just a thought, but the numbers on the left are Unix timestamps from yesterday and today.
May
16
revised Truth table reduction
Link to definition of term
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.