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| bio | website | gottwurfelt.wordpress.com |
|---|---|---|
| location | San Francisco, CA | |
| age | 29 | |
| visits | member for | 2 years, 10 months |
| seen | yesterday | |
| stats | profile views | 801 |
Quantitative analyst and math blogger.
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Feb 27 |
comment |
Solutions of $q=\frac{x}{y} +\frac{y}{z} + \frac{z}{x}$ s.t. $q \geq 3$ It doesn't. But let's say, for example, that I had $q = 731/210$, and I had rational numbers whose product is 1, say $2/3, 5/7, 21/10$, which add up to $731/210$. Then I would be frustrated because the numerators and denominators don't match up. But here we have $a = 2, b = 3, c = 5, d = 7$ and so we can write $10/15 + 15/21 + 21/10$, which has the matching numerators and denominators. |
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Feb 27 |
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Solutions of $q=\frac{x}{y} +\frac{y}{z} + \frac{z}{x}$ s.t. $q \geq 3$ Note that it's enough to show that there are three rational numbers with product 1 and sum $q$. If we have $x/y = a/b$ and $y/z = c/d$ with $a,b,c,d$ integers, then $z/x = bd/ac$. We can then write $q = (ac)/(bc) + (bc)/(bd) + (bd)/(ac)$ to give a solution of the form you seek. |
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Feb 21 |
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pseudo-random permutation of $[0,N)$ joriki: I think the idea is that this single function is supposed to work for all values of $N$. So one might have $\ldots, f(3,0) = 2, f(3,1) = 0, f(3,2) = 1, f(4,0) = 1, f(4,1) = 2, f(4,2) = 0, f(4,3) = 3, \ldots$ for example. |
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Feb 17 |
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What is a good book about math history? I bought it. But I probably wouldn't have except that right after it came out I happened to have a hundred dollars worth of miscellaneous coins which I brought to the bank, so it felt like free money. |
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Feb 16 |
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Are sines of primes dense in $[-1,1]?$ Also, the distribution of $sin(P)$ can be derived from the fact of the equidistribution of $P$ modulo $2\pi$. |
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Feb 14 |
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Ways to Score 18 Points in Football Excluding 2-point conversion This is fine. But it's a bit annoying to have to make sure that the number of PAT is less than or equal to the number of touchdowns. It might have been easier to have columns be safeties, field goals, touchdowns-without-PAT, and touchdowns-with-PAT, worth 2, 3, 6, and 7 points respectively. Just something to keep in mind if you're faced with similar problems in the future. |
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Feb 6 |
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is this line of thinking valid for quick solving? I would say that this is right, in that it can be turned into a rigorous proof, but with the caveat that you got lucky in assuming that $-1$ is small enough not to have an effect on the limit. In fact $\lim_{x \to \infty} (x^2/\sqrt{x^2-x}) - x = 1/2$. |
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Feb 5 |
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What does a particular part of this equation mean? Usually it's conventional to have the $C$ large and the $n$ and $k$ small -- that is, ${}_n C_k$. (I'm not sure I'd think of this as the usual notation; the ${n \choose k}$ notation seems more common among "grown up" mathematicians, although from talking to my students I think the $C$ notation is still taught at the high school level.) |
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Feb 4 |
answered | Most and least likely outcomes of a Bernoulli distribution experiment |
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Feb 3 |
answered | Finding $\lim_{n \to \infty }\sqrt[n]{b^{2^{-n}}-1}$ without L'hopital |
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Jan 30 |
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How to solve the recurrence relation $T(n) = 2T(\frac{2n}{3})$, where $T(0) = T(1) = 1$? The original poster didn't specify the initial conditions, but it seems reasonable to assume they're nontrivial. |
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Jan 30 |
answered | How to solve the recurrence relation $T(n) = 2T(\frac{2n}{3})$, where $T(0) = T(1) = 1$? |
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Jan 30 |
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Recurrence for perfect matchings revisited. Just a thought: bijective proofs and subtraction don't play well together. You might want to rewrite that as $A+E = B+C+D$ and look for a bijection between the sets counted by $A$ and $E$ and those counted by $B, C$ and $D$. |
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Jan 30 |
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vase question probability I think it would be nice if they were called vases, though. Vases make me think of flowers, urns make me think of cremation. |
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Jan 29 |
answered | Closest point to a unit circle from a point inside it |
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Jan 28 |
awarded | Nice Answer |
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Jan 27 |
answered | Chance of meeting in a bar |
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Jan 24 |
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How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859? Well, we can similarly start from the approximation $\sqrt{163} = 12.767$ and write $\sqrt{163} = (12767/1000)(1-3711/(163\times 10^6))^{-1/2}$; from the binomial series we'd get a better approximation of $\sqrt{163}$, which could presumably be made good enough to be useful. To get $\sqrt{163} \approx 12.767$ one could interpolate linearly between $\sqrt{161.29} = 12.7$ and $\sqrt{163.84} = 12.8$. |
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Jan 21 |
answered | What do High-Water Marks in Continued Fractions mean? |
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Jan 20 |
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Repeating last non-zero digits of factorial The answer may be in the references provided at oeis.org/A008904 |
