Example 9.9 A
daisy chain D(a b c d) after 3 double flypes is the
numerator of the tangle:
-(a+1).1.-(b+2).1.-(c+2).1.-(d+2).1.-(e+1)
= a.-(b+1).1.-(c+2).1.-(d+2).1.-(e+1)
= -a.b.-(c+1).1.-(d+2).1.-(e+1)
= a.-b.-c.-(d+1).1.-(e+1)
= -a.b.-c.d.-e
An extract on Continued Fractions from
David Fowler's book
Additional material including a proof of
proposition 9.4
More on the use of the Lagrange identity and the proof of 9.6 can
be found in a paper on rational tangles
by Goldman and Kauffman. See pages 315 and 316. See also Kauffman and
Lambropoulou.
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