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so a kid who's 14 in high school gets this version of the pythagorean theorem, which is a truly subtle and interesting proof, but in fact it's not a good way to start learning about mathematics.
一个14岁的孩子 在学校里学会了这样一套关于勾股定理的方法 这是一个非常微妙而有趣的证明 但这并非学习数学的一个很好的门路
draws an apollonian gasket: a fractal packing of circles with smaller circles, demonstrating descartes's theorem. http: / /en. wikipedia. org/ wiki/ apollonian_gasket http: / /en. wikipedia. org/ wiki/ descartes%27_theorem written by allan r. wilks and david bagley; 2002.
用很多小圆填充一个大圆, 演示笛卡儿圆圈理论。 由 allan r. wilks 和 david bagley 编写 。