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《江西教育》今年第3期《求“环形面积”的另一法》一文认为:“环形面积的计算,历来都采用大圆面积减去小圆面积。除了这种方法以外,还有一种比较独特而不落俗套的解法:在圆环的任意一处将圆环剪开后,展开成一个梯形,那么,这个梯形的下底就是大圆的周长;上底是小圆的周长;高是两圆半径之差。设大圆半径为R,小圆半径为r,圆环的面积=梯形的面积=1/2(2πR+2πr)×(R-r)=(Rπ+rπ)×(R-r)=(R+r)×(R-r)×π。”笔者认为,这样的计算公式虽然无误,但推导方法却值得商榷。
“Jiangxi Education” No. 3 of this year, “seeking” ring area “another article” that: “The calculation of the ring area, has always been using a large circular area minus the small circular area.In addition to this method, there is a more unique Unconventional solution: the ring at any place cut the ring, expand into a trapezoid, then the bottom of the trapezoid is the circumference of the great circle; the upper end is the circumference of a small circle; high is The radius of the two circles is the radius of the circle R, the radius of the circle r, the area of the circle = the area of the trapezoid = 1/2 (2πR + 2πr) × (Rr) = (Rπ + rπ) × (Rr) = (R + r) × (Rr) × π. ”The author believes that although this formula is correct, but the derivation method is debatable.