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Nov
25
comment Prove that every practical number is either a power of two or a power of two times a non-trivial polygonal number
@half-integerfan, I've added lists of 1000 and 1000000 practical numbers to my personal site at cheddarmonk.org/maths/practical_numbers/… and obvious substitution. I will refresh my memory on the current comment submission process for OEIS at a later date.
Nov
8
comment Representing everywhere a camera can see as a matrix
you can test a point $Q=(x_Q, y_Q, z_Q)$ against the near and far planes by simply comparing $z_Q$ to the near and far clipping distances; you can clip against the side planes by comparing $x_Q / z_Q$ to $\pm\tan (\theta_w/2)$ where $\theta_w$ is the angular width; and you can clip against the top and bottom planes by comparing $y_Q / z_Q$ to $\pm\tan (\theta_h/2)$ where $\theta_h$ is the angular height.
Nov
8
comment Representing everywhere a camera can see as a matrix
@Imray, the frustrum is bounded by 6 planes. Testing which side of a plane a point is on comes down to looking at the sign of a dot product. (E.g. if the plane is defined by a point $P$ in the plane and its normal $N$ then you can test which side a point $Q$ is by looking at the sign of $(Q-P).N$). It wouldn't surprise me, though, if actual implementations take a different approach. If you transform the world such that your camera is positioned at the origin and looks along the $z$-axis, with the up vector pointing along the $y$-axis, then (cont)
Nov
7
comment Probabilty to win in die rolling game
Thanks for editing to add your ideas. The point at which you're going wrong is to interpret the question as asking for a probability which relates to a single die roll. It's actually asking for the probability that you lose on the first die roll (which you correctly state to be $k/N$), or that you lose on your next die roll, or a subsequent one. I hope that makes it clearer what you should be recursing on.
Nov
5
comment Dead presidents
I think the only reasonable answer to this question is that it's not well posed. If you're supposed to pretend you don't know the death dates, shouldn't you also pretend that you don't know how many are still alive? So the person who posed it should specify precisely what information you have as prior knowledge.
Nov
4
comment is this operating procedure an Abelian Group?
@K.L., yes, each element is self-inverse.
Nov
2
comment Generator of a subgroup of a cyclic group
The title is the only thing about the question which shows in most contexts, so it's worth having a title which gives a clue as to what the question is about.
Nov
1
comment What is the official proof (if there is any) for the area of a circle of radius 'r'?
Related question: math.stackexchange.com/q/44631/5676
Oct
31
comment How to show that the order in which multiple sums are performed does not matter
Probably not sufficiently rigorous for your purposes, but the first of Knuth's Two notes on notation is relevant.
Oct
31
comment Probability to find A
The answers to all three questions are A, axiomatically.
Oct
26
comment Freeman Dyson's example of an unprovable truth
That fills the gap nicely. Thanks.
Oct
26
comment Freeman Dyson's example of an unprovable truth
I don't see the relevance of your comments on "unlikely" true statements. The contrapositive of "it seems likely, so it must be true" is not "it seems unlikely, so it must be false".
Oct
24
comment Show that if $F$ is multiplicative, then $f$ is multiplicative
How do you justify $$\sum_{d\mid n_1n_2} \mu(d)F(n_1n_2/d) = \sum_{d\mid n_1n_2} \mu(d)F(n_1/d)F(n_2/d)$$?
Oct
23
comment Special case of the Schroeder-Bernstein Theorem
I think you mean $f(U)'$, not $f(U')$, but what does the prime signify in this book? Is it set complement?
Oct
17
comment $f(x+y)=f(x)f(y)$
This question is a question on an open contest and the contest organisation has requested that it be closed until the contest finishes.
Oct
16
comment Graph Cut Problem
Is friendship symmetric?
Oct
15
comment How does my professor come up with the recursive case in this algorithm analysis?
As an aside, the "recursive array" datastructure which has a non-constant append cost is not the best choice for this situation.
Oct
15
comment How does my professor come up with the recursive case in this algorithm analysis?
The bit you quote talks about the cost: it's explaining the $+m+1$ later in the expression.
Oct
15
comment How does my professor come up with the recursive case in this algorithm analysis?
You're picking up the wrong $m+1$ there.
Oct
15
comment Approximations other than taylor series and pade approximation
Is there a specific reason for needing a function which approximates it as opposed to an iterative solver (e.g. Newton-Raphson)?