Ben Alpert
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# 66 Comments

 Oct 18 comment Probability that a stick randomly broken in two places can form a triangle @hlapointe If the first break gives a stick with length $x$, then the remaining length is $1-x$. Splitting that randomly is the same as multiplying by a random number $y$ between $0$ and $1$, so we get $y(1-x)$. Apr 10 comment How can you prove that the square root of two is irrational? If $p = 2^k m$ where $m$ is odd, then $p^2 = 2^{2k} m^2$ (where $m^2$ is still odd). Dec 2 comment Kleene Closure and determining whether a string x is in a set @BrianM.Scott Oops, my bad. I somehow missed the first paragraph and only read the third. Dec 2 comment Kleene Closure and determining whether a string x is in a set For the first set, you could also use a parity argument on the length of the string. Jul 13 comment Can two sets have same AM, GM, HM? Very nice solution. Sep 19 comment Mandelbrot-like sets for functions other than $f(z)=z^2+c$? @Isaac: Many of your pictures seem to be missing now… Jun 27 comment Choose K items from N in a circle No problem, hopefully now it's a little easier to understand! Jun 23 comment Use of “inverse” to mean reciprocal Yes, I understood that the reciprocal is a type of inverse, but "inverse" seems overly general to specify a reciprocal relationship. Jun 22 comment Finding $\sin(4a)$ if we know $\cos a$ Please ask your second problem as an entirely new question instead of as an edit to this one. Jun 21 comment Proving Stewart's theorem without trig Thanks, your answer is definitely good enough for my purposes. Good night! Jun 21 comment Proving Stewart's theorem without trig Very nice, thanks! May 15 comment Function $F$ that $F(x)+F(-x)=\lim_{y\rightarrow\infty}F(y), \forall x \in \mathbb{R}$ @Tim: Might want to change the title too. May 10 comment Calculate intersection of 2 points @J.M. I'm pretty sure Ross Millikan interpreted it right. You have two points and two slopes given as angles from the vertical ($\pi/2$) and want the intersection between the two lines thus determined. Apr 28 comment Why the name 'FACTORIAL'? But that's true of other numbers (both smaller and larger) that aren't the factorial. Apr 26 comment Calculating the highest possible damage achievable using 6 items from a pool of ~25 Probably belongs on SO. Apr 25 comment Inclusion-exclusion principle: Number of integer solutions to equations @DAK: Reread Gerry's last paragraph. For the intersection of $A_1$ and $A_2$, it's equivalent to solving $v_1+v_2+y_3+y_4=5$ with $v_1, v_2, y_3, y_4 \ge 0$. Just like the number of solutions to solve $y_1+y_2+y_3+y_4 = 12$ is $C(15,3)$, the number of solutions to that equation (and the size of the $\lvert A_1 \cap A_2 \rvert$ set) is $C(8,3)$. Apr 25 comment Inclusion-exclusion principle: Number of integer solutions to equations I agree, I think it's $C(12 + 4 - 1, 3) = C(15,3)$. Apr 13 comment Can (x'y' + xy) be simplified? @Brandon: You should probably write that as an answer. Apr 13 comment Draw customized (calculus) graphs like these? Not sure whether to flag it, but I have enough rep to retag stuff so I got rid of the graph-theory tag. Mar 31 comment Interpreting “lying on the parabolas” Out of curiosity, how do you get Mathematica to make that?