Timeline for Structures in the plot of the “squareness” of numbers
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Nov 22, 2016 at 11:46 | answer | added | Aaron Meyerowitz | timeline score: 4 | |
| Nov 21, 2016 at 23:59 | vote | accept | Joseph O'Rourke | ||
| Nov 21, 2016 at 18:37 | answer | added | მამუკა ჯიბლაძე | timeline score: 14 | |
| Nov 21, 2016 at 17:29 | answer | added | Gottfried Helms | timeline score: 13 | |
| Nov 21, 2016 at 11:26 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 317 characters in body
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| Nov 21, 2016 at 3:25 | answer | added | Lucia | timeline score: 22 | |
| Nov 21, 2016 at 1:35 | comment | added | Joseph O'Rourke | @PatDevlin: Yes, you are correct, the $\frac{1}{3}$ density change is evident if I plot beyond $n=10^5$. (But---sorry---no more plots tonight.) | |
| Nov 21, 2016 at 1:31 | comment | added | Pat Devlin | It looks like when you only plot the values for odd $n$ the line at 1/2 goes away, but there's a faint line at 1/3. I bet if you plotted the numbers not divisible by 2 or 3, there would be only a faint line at 1/5. | |
| Nov 21, 2016 at 1:27 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 283 characters in body
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| Nov 21, 2016 at 1:23 | comment | added | Pat Devlin | I'm curious about the densities here. For fixed $x \in (0,1)$, define $D(x)$ to be the set of integers with ratio at most $x$. Then could you show us a plot of $f(x,N) = | D(x) \cap [N] | / |N|$? Ideally a few plots. Some showing this as a function of $x$ and $N$ very large. And some showing this as a function of $N$ with $x$ fixed. Pat "also wondering about the middle names" Devlin | |
| Nov 21, 2016 at 1:16 | comment | added | user78249 | @GerhardPaseman I couldn't resist. James "wondering why Gerhard Paseman always does this" Nixon, 2016.11.20 | |
| Nov 21, 2016 at 1:16 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added another example.
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| Nov 21, 2016 at 1:09 | comment | added | Gerhard Paseman | What happens if you make the same plot but leaving out all of the even numbers? Maybe that will affect or explain the density you see in the current plot. Gerhard "Is Wanting More Pretty Pictures" Paseman, 2016.11.20. | |
| Nov 21, 2016 at 0:55 | comment | added | Gerhard Paseman | I think it is clearer to say that $r=d^2/n$ for $d$ the largest divisor of $n$ with $d^2 \leq n$, assuming I interpret your statement correctly. Just seeing d^2 makes me think of conic sections; this algebraic reformulation might help answer some of your questions. Gerhard "Except For The Density Change" Paseman, 2016.11.20. | |
| Nov 21, 2016 at 0:48 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Puncutation.
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| Nov 21, 2016 at 0:46 | comment | added | user78249 | Wow, this is a beautiful plot. It's amazing how you can see hyperbolas and curves but they break apart at discontinuous rates. Nothing mathematical to add, just that it's a really cool plot. Reminds me of fractals. | |
| Nov 21, 2016 at 0:07 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |