■等面単体の体積(その179)

  (4-a^2)(4-c^2)=16λ^2

  1/λ^2=4/(4-a^2)+4/(4-b^2)+4/(4-c^2)

=4{(4-a^2)(4-b^2)+(4-b^2)(4-c^2)+(4-c^2)(4-a^2)}/(4-a^2)(4-b^2)(4-c^2)

  (4-a^2)(4-c^2)=4(4-a^2)(4-b^2)(4-c^2)/{(4-a^2)(4-b^2)+(4-b^2)(4-c^2)+(4-c^2)(4-a^2)}

{(4-a^2)(4-b^2)+(4-b^2)(4-c^2)+(4-c^2)(4-a^2)}=4(4-b^2)

{(8-a^2-c^2)(4-b^2)+(4-c^2)(4-a^2)}=4(4-b^2)

b^2(4-b^2)+(4-c^2)(4-a^2)}=4(4-b^2)

(4-c^2)(4-a^2)=(4-b^2)^2

(4-c^2)(-4+c^2+b^2)=(4-b^2)^2

(4-c^2)^2-b^2(4-c^2)+(4-b^2)^2=0

4-c^2=1/2{b^2-(b^4-4(4-b^2)^2)^1/2}

4-c^2=1/2{b^2-(-64+32b^2-3b^4)^1/2}

4-c^2=1/2{b^2-{(3b^2-8)(8-b^2))^1/2}

c^2=1/2{8-b^2+{(3b^2-8)(8-b^2))^1/2}

a^2=1/2{8-b^2-{(3b^2-8)(8-b^2))^1/2}

===================================