Timeline for Is there an elementary proof of a result about the parity of the period of the repeating block in the continued fraction expansion of square roots
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| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://math.berkeley.edu/ with https://math.berkeley.edu/
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| Oct 8, 2011 at 19:11 | comment | added | Ian Agol | @joro: I think the question is for square roots of primes. | |
| Jan 30, 2010 at 19:43 | comment | added | Jason Smith | Oh, Allen Hatcher has some nice info on this. Thanks Allen. | |
| Jan 30, 2010 at 19:04 | comment | added | Jason Smith | Thank you Agol! My proof as stated in the question uses only what I learned from reading C.D. Olds' 'Continued Fractions' and Edward J. Barbeau's 'Pell's Equation' and a lot of thinking. I have virtually no exposure to Faray Diagrams but have a good foundation in modern algebra. Is there any books at the master's level that you would suggest so that I can understand your answer? | |
| Jan 30, 2010 at 5:49 | comment | added | Allen Hatcher | Nice pictures! I taught an undergraduate number theory course from this point of view (The Farey diagram) last semester, the notes for which are available here: math.cornell.edu/~hatcher/TN/TNpage.html See Chapters 1 and 2 in particular. Conway's topographs also form an integral part of the story. (My apologies for the shameless self-promotion!) When I revise the notes I'll have to add the nice fact discussed in the original post above, which was new to me. Thanks to all for the great answers! | |
| Jan 30, 2010 at 5:43 | comment | added | S. Carnahan♦ | There is a nice dual picture using Ford circles. I think if you draw a vertical line from $\pm\sqrt{p}$ to $i\infty$, the Ford circles that it intersects are tangent to the real line at the convergents. | |
| Jan 30, 2010 at 4:38 | history | edited | Ian Agol | CC BY-SA 2.5 |
fixed matrices
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| Jan 30, 2010 at 4:27 | history | edited | Ian Agol | CC BY-SA 2.5 |
added 319 characters in body
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| Jan 30, 2010 at 2:03 | history | answered | Ian Agol | CC BY-SA 2.5 |