■ピラミッドの傾斜角(その6)

 (その3)(その4)の解は

  b^2=h(h−1)^2/(h−2)

  2bb’={(3h^2−4h+1)(h−2)−(h^3−2h^2+h)}/(h−2)^2

=2(h^3−4h^2+4h−1)/(h−2)^2

=2(h−1)(h^2−3h+1)/(h−2)^2

h=(3+√5)/2=τ+1=τ^2

  a=b/(h−1)={h/(h−2)}^1/2

傾斜角は

  arctan(h/a)=arctan{h(h−2)}^1/2

=arctan(√τ)

 (その5)の傾斜角も

  arctan(h/a)=arctan{h(h−2)}^1/2

  h=2.83929

で計算される.

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