■基本単体の直角三角錐分割(その6)

 1,1,1,1,1

  2,2,1,3

   3,1,2

    1,1,

     0

はそれぞれ,

  (−1,0),(0,1),(1,2),(2,3),(2,4)

    (−1,1),(0,2),(1,3),(2,4)

      (−1,2),(0,3),(1,4)

        (−1,3),(0,4)

           (−1,4)

に対応していて,(1,4)=2,(2,4)=3より,

  AB^2=1/(1,4)=1/2

  BE^2=1/(1,4)(2,4)=1/6

  EC^2=1/(2,4)=1/3

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 (s,s)=0,(s,s+1)=1

2行目(s−1,s+1)の積

 (−1,1)(0,2)=sec^2α

 (0,2)(1,3)=sec^2β

 (1,3)(2,4)=sec^2γ

 また,

  (t,u)(s,v)+(u,s)(t,v)+(s,t)(u,v)=0より

  (s,t)={(s,t−1)(s+1,t)−1}/(s+1,t−1)

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