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一九八八年全国高中数学联赛第一试试题中,有这样一道选择题: 已知:三个平面α、β、γ,每两个平面之间的夹角都是θ,且α∩β=α,β∩γ=b,γ∪α=c.若有命题甲:θ>π/3 命题乙:a、b、c相交于一点.则(A)甲是乙的充分条件但不必要. (B)甲是乙的必要条件但不充分. (C)甲是乙的充分必要条件. (D)(A)、(B)、(C)都不对. 不难证明甲是乙的充分条件.在证充分性之前值得指出:现行教材没有明确提到两平面间的夹角,但通常都是指两平面相交所成的诸二面角的平面角中不
In the first question of the National High School Mathematics League in 1988, there was such a multiple-choice question: Known: The three planes α, β, γ, the angle between each two planes are θ, and α ∩ β =α,β∩γ=b,γ∪α=c. If there is a proposition A:θ>π/3 Proposition B: a, b, c intersect at one point. Then (A) A is a sufficient condition for B but not necessary (B) A is a necessary but not sufficient condition for B. (C) A is a sufficient and necessary condition for B. (D) (A), (B), (C) are not correct. It is not difficult to prove that A is B’s full. Conditions. It is worth pointing out before the adequacy: the current textbook does not explicitly mention the angle between the two planes, but usually refers to the plane angles of the dihedral angles where the two planes intersect.