Let L (a, b) denote the perimeter of an ellipe with semi-axes a, b. It is well known that π (α + b) ≤ L(a,b) ≤ 2π((a~2+b~2)/2)/(1/2)，with equality if， and only if, b = a. There are several proofs of this remarkable fact in the literature; see, for example, [1], [2] and [3]. The aim of this note is to compile a proof suitable for high school students as much as possible. We start with the standard parametrisation x = a cos t,y = b sin t which gives rise to L (a, b) =4∫(a~2cos~2t + b~2 sin~2t)/(1/2)dt.
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机译：令L（a，b）表示具有半轴a，b的椭圆的周长。众所周知，π（α+ b）≤L（a，b）≤2π（（a〜2 + b〜2）/ 2）/（1/2），当且仅当b =一种。文献中有许多证据证明了这一非凡的事实。参见例如[1]，[2]和[3]。本注释的目的是尽可能地汇编适合高中生的证明。我们从标准参数化x = a cos t，y = b sin t开始，得出L（a，b）=4∫（a〜2cos〜2t + b〜2 sin〜2t）/（1/2） dt。
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