I had already talked on √2 based on vilvam /bael twig and its leaves.
The continued fraction was
[1,1,2,1,2,1,2, . . . . . . ]
It takes an expert to say that √3 is due to wind on √2 leaves.
What will happen when wind blows on a bael twig. The two leaves will make a namaste and come back to the original state.
Therefore the continued fraction of √3 is
[1,1,1,1,2,1,1,1,2, . . . . . .]
Hence proved.
If [1;1,2,1,2,1,2....] is replaced with 1 for alternative 2s; 1st and 3rd and 5th and so on we get [1;1,1,1,2,1,1,1,2....].
ReplyDeleteThe first is root 2.
The second is root 3.
If we replace all 2 with 1 then we get [1;1,1,1,1,1.....].
The near above is fibonacci number.
Always namaste is golden ratio.
I am writing from memory.
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