两正数四种平均的几何统一表示及加强

Unified and Strengthened Form For Two Positive Numbers of Four Kind Means

将两正数a、b的调和、几何、算术、方幂平均统一为:T(a,b,θ)=a2cos2θ+b2sin2θ(θ<a≤b,0≤θ≤π/2).并给出这四种平均的加强.

For the harmonic mean, geometric mean, arithmetic mean, square powers mean of the two positive numbers： a, b, the unified form is given： T（a,b,θ）=√a^2＋cos^2θ＋b^2sin^2θ（θ〈a≤b,0≤θ≤π/2）. and the strengthen forms of the four kind means are also given.