■正四面体の断面(その19)

[1]3次元

  b3=−b2・a2/a3

  b2=−a1/(3a2)

  b3=a1/(3a3)

[2]5次元

  b5=−b4・a4/a5

  b4=−b3・3a3/5a4

  b5=b3・3a3/5a4・a4/a5=b3・3a3/5a5

  b3=−b2・a2/a3

  b4=b2・a2/a3・3a3/5a4=b2・3a2/5a4

  b5=b3・3a3/5a5=−b2・3a2/5a5

  b2=−a1/3a2

  b3=a1/3a3

  b4=−a1/5a4

  b5=a1/5a5

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[3]4次元

  b4=−b3・a3/a4

  b3=−b2・a2/(2a3)

  b4=b2・a2/(2a3)・a3/a4=b2・a2/(2a4)

  b2=−a1/a2

  b3=a1/(2a3)

  b4=−a1/(2a4)

[4]6次元

  b6=−b5・a5/a6

  b5=−b4・(2a4)/(3a5)

  b6=−b5・a5/a6=b4・(2a4)/3a6

  b4=−b3・a3/a4

  b5=b3・2a3/3a5

  b6=−b3・(2a3)/3a6

  b3=−b2・a2/2a3

  b4=b2・a2/2a4

  b5=−b2・a2/3a5

  b6=b2・a2/3a6

  b2=−a1/a2

  b3=a1/2a3

  b4=−a1/2a4

  b5=a1/3a5

  b6=−a1/3a6

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[まとめ]

[1]奇数次元では(−3,3)→(−3,3,−5,5)

[2]偶数次元では(−1,2,−2)→(−1,2,−2,3,−3)

と係数は2項単位で変化する.

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