■等面単体の体積(その256)

  (x−2)^2+y^2+z^2=4

  (x−3/2)^2+(y−(√5)/2)^2+(z−(√10)/2)^2=6

  (x−1)^2+(y−√5)^2+z^2=6

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[1]x=3s/2+2,y=(√5)s/2,z=(√10)s/2

  9s^2/4+5s^2/4+10s^2/4=4

  s^2=2/3,これは誤りではない.

  (3s+1)^2/4+5(s−1)^2/4+10(s−1)^2/4=6

  (3s+2)^2/4+5(s−2)^2/4+10s^2/4=6

  (3s+1)^2+5(s−1)^2+10(s−1)^2=24

  (3s+2)^2+5(s−2)^2+10s^2=24

  24s^2−24s+16=24

  24s^2−8s+24=24は満たさない.

[2]x=3t/2+1,y=(√5)t/2+√5,z=(√10)t/2

  9t^2/4+5t^2/4+10t^2/4=6,t^2=1

  (3t−2)^2/4+5(t+2)^2/4+10t^2/4=4

  (3t−1)^2/4+5(t+1)^2/4+10t^2/4=4

はNG.

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