| 圆的面积公式的新证明——验证圆的面积公式S=πr^2 |
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| 引用本文： | 陈超霞,李晓培.圆的面积公式的新证明——验证圆的面积公式S=πr^2[J].湛江师范学院学报,2013(6):31-33. |
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| 作者姓名： | 陈超霞 李晓培 |
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| 作者单位： | 湛江师范学院数学与计算科学学院,广东湛江524048 |
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| 摘 要： | 本文应用阿基米德的内外正多边形逼近法和开普勒的无穷分割法，站在后人的肩膀上，运用极限理论，洛比达法则，以及收敛法则，夹逼法则，三角函数等近代数学的办法，来为开普勒对上述问题做个解释，从而验证圆的面积计算公式确实为S=πr^2
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| 关 键 词： | 圆的面积计算 逼近 无穷分割 |
A New Proof of the Area Formula of a Circle |
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| CHEN Chaoxia,LI Xiaopei.A New Proof of the Area Formula of a Circle[J].Journal of Zhanjiang Normal College,2013(6):31-33. |
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| Authors: | CHEN Chaoxia LI Xiaopei |
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| Institution: | (School of Mathematics and Computational Science,Zhanjiang Normal University, Zhanjiang 524048, Guangdong, China) |
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| Abstract: | In this paper , by applying the regular polygon approximation method of Archimedes and the infinite partition method of Kepler Johannes, overlooking the previous by standing on the shoulder of the latter, we use the limit theorem, the Robita rule, the convergence rule, the clamping force principle,trigo- nometric function and more modern mathematics to experience. Also, the formula for calculating the area of a circle is validated. |
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| Keywords: | calculating of area of a circle approximation infinite partition |
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