Timeline for Another question about the golden ratio and other numbers
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 19, 2017 at 5:07 | answer | added | T. Amdeberhan | timeline score: 3 | |
| Jan 17, 2017 at 22:11 | comment | added | Kevin Buzzard | Clarification: by "the power series" I mean the one on the denominator, not the one with the $c_i$ in. | |
| Jan 17, 2017 at 20:02 | comment | added | Kevin Buzzard | What's going on in general presumably is that the ratio is simply the reciprocal of the first zero of the power series, which for the golden ratio will just be some random (negative, in this case) real (the power series clearly converges for $|x|<1$). For the rational numbers the zero will be some algebraic number satisfying some funky polynomial whose coefficients are related to floor(r),floor(2r),floor(3r)... . | |
| Jan 17, 2017 at 19:11 | comment | added | Richard Stanley | One can simplify $L(8/5)$ to the largest root of $x^3+x^2+2$. | |
| Jan 17, 2017 at 17:42 | comment | added | Kevin Buzzard | The rational ones are easy because everything is a rational function and hence the coefficients are solutions to a recurrence relation. For example $L(8/5)$ is just the smallest root of $x^8 + 3*x^7 + 4*x^6 + 6*x^5 + 8*x^4 + 7*x^3 + 5*x^2 + 4*x + 2$ (sorry for computer notation). | |
| Jan 17, 2017 at 17:29 | history | edited | Douglas Zare | CC BY-SA 3.0 |
Added link and data and clarified question.
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| Jan 17, 2017 at 15:54 | history | asked | Clark Kimberling | CC BY-SA 3.0 |