- 962 名前：120ﾟ-θ） = 2t/(√3 +t),
AP2 = AP1 sin(60ﾟ+θ)/sin(60ﾟ-θ)
= AP1 sin(120ﾟ-θ)/sin(60ﾟ-θ)
= sinθ / sin(60ﾟ-θ)
= 2t/(√3 -t),
S(t) = ⊿P0P1A - ⊿AP1P2
= (1/2)sin(∠A) AP1 (1-AP2)
= (1/2)((√3)/2)(2t/(√3 +t))((√3 -3t)/(√3 -t))
= (3/2)t(1-t√3)/(3-tt),
t = 2√6 - √3 のとき極大 (3√3 -2√6)/4 = 0.074293
θ = 16.5505°
・30ﾟ<θ<60°のとき
AP1 = sinθ / sin(120ﾟ-θ) = 2t/(√3 +t),
BP1 = 1 - AP1 = (√3 -t)/(√3 +t),
BP2 = BP1 / AP1 = (√3 -t)/2t,
S(t) = ⊿P0P1B - ⊿BP1P2
= (1/2)sin(∠B) BP1 (1-BP2)
= (1/2)((√3)/2)(√3 -t)(3t-√3)/(t(√3 +t))
= (3/8)(√3 -t)(t√3 -1)/(t(√3 +t)),
t = (2√6 +√3)/7 のとき極大 (3√3 -2√6)/4 = 0.074293
θ = 43.4495° [] - [ここ壊れてます]
|
 |
