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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