Timeline for Elementary + short + useful
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 2 at 14:18 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
minor typos
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| Dec 20, 2013 at 7:29 | comment | added | smyrlis | @VictorProtsak: See edited version of my answer, were historical data are added. | |
| Dec 20, 2013 at 7:27 | history | edited | smyrlis | CC BY-SA 3.0 |
Added historical data.
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| Dec 20, 2013 at 1:57 | comment | added | Todd Trimble | @VictorProtsak I've also heard it said that the proof of irrationality of $\sqrt{5}$, based on the geometry of the pentagon, may well have preceded that of $\sqrt{2}$. | |
| Dec 20, 2013 at 1:56 | comment | added | Todd Trimble | @BenjaminDickman I agree with you; perhaps smyrlis would like to add more details. | |
| Dec 20, 2013 at 1:46 | comment | added | Victor Protsak | In fact, there is some controversy as to whether the "traditional" even-odd reductio ad absurdum proof was the first one. Many sources assert that the original proof extended to irrationality of $\sqrt{d}$ for $d<17, d\ne 1,4,9,16,$ which would be consistent with not using elementary divisibility properties of primes. Also, some authors believe that a geometric proof involving the diagonal and the side of a square (the one that is equivalent to the non-termination of the continued fraction expansion of $\sqrt{2}-1$) was invented concurrently with or earlier than the even-odd argument. | |
| Dec 19, 2013 at 23:44 | comment | added | Benjamin Dickman | @ToddTrimble Agreed; I think What would you do? ought to encompass more than just the stated theorem... | |
| Dec 19, 2013 at 23:15 | comment | added | Todd Trimble | Well, there are by now many proofs, lending themselves to different directions and generalizations, and such might make for an interesting 30-minute lecture to undergraduates. | |
| S Dec 19, 2013 at 22:45 | history | answered | smyrlis | CC BY-SA 3.0 | |
| S Dec 19, 2013 at 22:45 | history | made wiki | Post Made Community Wiki by smyrlis |