DOWNLOAD-DESKTOP-NOTEBOOK.nb (228 KB)
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What an interesting problem with intuitive simulation and traceable proof !
I found it’s the perfect example to teach my kids some math.
Shenghui, Good job！
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I am glad you find it interesting and joyful!
My daughters, as middle school students, first found the mathematical constant Pi interesting and memorized dozens of its digits. However, Pi is primarily associated with circles, angles, and rotations, and that’s about it.
Later, I bought a book, e: The Story of a Number, for my daughters, and sometimes I would read it myself.
In fact, e is a truly magical constant that does widely appear and frequently be used.