Timeline for "Harmonacci" recurrence and identities for $\pi$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2013 at 6:24 | comment | added | Victor P | Aaron - Cute indeed. | |
| Jan 18, 2013 at 19:24 | vote | accept | Victor P | ||
| Jan 18, 2013 at 13:11 | comment | added | Aaron Meyerowitz | A cute reformulation: start with a unit square, put another next to it on the left, then a 2 x 1/2 along the top and continue always adding a unit area rectangle alternating top and left. What is the limiting ratio of length to height? | |
| Jan 18, 2013 at 10:42 | answer | added | Felix Janda | timeline score: 23 | |
| Jan 18, 2013 at 10:05 | comment | added | Sylvain JULIEN | For $a_0=2n+1$, the numerator of the limit $l_{2n+1}$ seems to be $(1\times 3\times...(2n+1))^2\pi$ and its denominator $2^{2n}\times D(l_{2n-1})$, where $D(l_{2n-1})$ is the denominator of $l_{2n-1}$. And it seems that $l_{2n}=2^{2n}/l_{2n-1}$. Maybe a proof by reccurence could be achieved. | |
| Jan 18, 2013 at 8:59 | comment | added | Nikita Sidorov | So, in terms of continued fractions, we have $a_{n+1}=[a_{n-1}; a_{n-2},\dots, a_2, a_1, a_0, a_1]$. | |
| Jan 18, 2013 at 8:08 | comment | added | Dirk | +1 for "Harmonacci" | |
| Jan 18, 2013 at 7:22 | history | edited | Victor P | CC BY-SA 3.0 |
deleted 3 characters in body; added 27 characters in body
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| Jan 18, 2013 at 7:11 | history | asked | Victor P | CC BY-SA 3.0 |