Wikipedia:Reference desk/Archives/Mathematics/2014 December 13
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December 13
[edit]Meandric numbers
[edit]
According to Meander (mathematics), and (sequence A005315 in the OEIS), the third meandic number is eight. Ok, so I can find four distinct meanders, A1 to A4, with 23 crossings and along with their horizontal reflections, B1 to B4, make the required eight. But wait, some of them, C2 to C4, have a vertical reflection not homomorphic to any of the eight, and along with their horizontal reflections, D2 to D4, make a total of 14. What am I missing? SpinningSpark 11:29, 13 December 2014 (UTC)
- The pdf linked in the article gives all 8. The problem is that yours are crossing the line 8 times, not 6. (It's 2n not 2^n, so you should have 6 crossings)Phoenixia1177 (talk) 12:59, 13 December 2014 (UTC)
- Ah, thanks. I knew it had to be something simple. Just for the record, I found quite a few more with eight crossings after posting the diagram. SpinningSpark 13:17, 13 December 2014 (UTC)