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Sep
1
revised Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
Elaborated.
Sep
1
comment 1, 5, 9, 13, 17, 21,…
@JoshuaTaylor: That's the best.
Sep
1
comment 1, 5, 9, 13, 17, 21,…
Why not flip it around? $\{n | n=4k-3 \; \forall k \in \mathbb{N}\}$. I think this is more straightforward. Or a little more simply, $\{n | n=4k-3, \; k \in \mathbb{N}\}$.
Aug
30
reviewed Approve Function that transforms the interval $[a,b]$ into $[0,1]$
Aug
29
awarded  Nice Answer
Aug
28
reviewed Reject Minesweeper probability
Aug
28
comment Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
@HagenvonEitzen: That's true, greater rigor would mean a little more complexity. However, I see this as one of those things that is intuitively true and simple, which also holds up under deeper analysis.
Aug
28
answered Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142.
Aug
21
reviewed Approve How to calculate the cardinality of the complement of two countable sets of reals?
Aug
15
reviewed Approve Convergence of improper integral $\int_{0}^{\frac{\pi}{6}}\dfrac{x}{\sqrt{1-2\sin x}}dx$
Aug
13
reviewed Reject Cosine formula to show if an angle is obtuse or acute
Aug
9
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
Finally solved it! I contest your claim that it is "an easy solution"! Took me several hours. But I did it! So, again, thank you very much for your input. Turned out to be just what I needed. :)
Aug
8
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
Had a key insight: $M\left[ \begin{array}{c}1\\0\\0\end{array} \right] = -\vec{v}$ and I've very nearly got the solution. Just need to find a bug or two.
Aug
8
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
After working on this for a couple hours, I challenge you to find a complete solution.
Aug
7
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
I thought about it more, and I realized that if I can get the last three equations to have the same three variables each, then that immediately leads to the full solution. Which is slightly less daunting than substitutions all the way down. Thanks for your answer! It's really helped me actually tackle my problem. :)
Aug
6
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
That was the first thing I did: get $a=\sqrt{1+d^2+g^2}$ and likewise for the next two (which are actually equal to $-1$, not $1$). But then the next equations get messy fast. $ab-de-gh=0 \Rightarrow (1+d^2+g^2)(-1+e^2+h^2) = d^2e^2 + 2degh + g^2h^2$. I can make this a quadratic in $d$ to eliminate the fourth variable, but I still have five more variables to go and I already have a really messy equation here. Doing the same for the fifth equation allows me to eliminate $g$, I think. Still need to eliminate $e,f,h,i$. It's horrible.
Aug
5
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
I let $M = \left[ \begin{array}{ccc}a&b&c \\ d&e&f \\ g&h&i \end{array} \right]$ and $\vec{v} = \left[ \begin{array}{c}x_1 \\ x_2 \\ x_3 \end{array} \right]$ and got a system of nine non-linear equations. $$\begin{align*}a^2-d^2-g^2 &= 1 \\ b^2-e^2-h^2 &= 1 \\ c^2-f^2-i^2 &= 1 \\ ab-de-gh &= 0 \\ ac-df-gi &= 0 \\ bc-ef-hi &= 0 \\ ax_1+bx_2+cx_3 &= 1 \\ dx_1+ex_2+fx_3 &= 0 \\ gx_1+hx_2+ix_3 &= 0 \end{align*}$$ I'm sure this is solvable, but I'd like to be able to solve it without the help of a software package. I started doing some substitutions, but it quickly gets very messy.
Aug
4
comment On the hyperboloid model, if the point $\mathbf{v}$ gets translated to the origin, then where does the point $\mathbf{x}$ go?
@LeeMosher: I'm having difficulty even figuring out what $SO(2,1)$ is, and I only vaguely understand Lorentz transformations at best. The paucity of examples is being a real problem too. I learn best when given an example, the general case, and then another example.
Aug
4
reviewed Approve Is “angle between two directions” appropriate?
Aug
4
reviewed Approve 10th derivative of a function