几何原本

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• leephillips · 2021 年

  读起来很有趣也很愉快。我觉得很有启发性的是，今天仍然有人（不过几代人之前更多）通过欧几里得的《几何原本》（Euclid's Elements，通常是译本）来学习几何。我真的很喜欢“人们至今还在用一本 2000 多年前的书学数学”这种感觉。

  Interesting and pleasant to read. I find it inspiring that some people today (but more a couple of generations ago) still learn geometry from (usually translations of) Euclid’s Elements. I just love the idea that people still study math from a book more than 2,000 years old.

• morelisp · 2022 年

  （已经有人发了《怎样解题》（How to Solve It），这本来是我在这个论坛上的首推。）《庄子》，最好至少读两个译本。《几何原本》（就是欧几里得那本）。《过程与实在》（Process and Reality）对我的思维影响最大，但它也是我读过的最晦涩难懂的书之一。早晚去啃啃看吧。

  (Someone already posted How to Solve It which would be my first recommendation on this forum.) The Zhuangzi, probably at least two translations. The Elements (that is, Euclid's). Process and Reality has had the most impact on my thinking but it's one of the most unapproachable things I've ever read. Get there eventually.

• zoul · 2011 年

  有一本讲庞加莱猜想（Poincaré conjecture）的书非常棒，从欧几里得《几何原本》中的几何源头一直讲到佩雷尔曼（Perelman）的证明：http://books.google.com/books?id=kM8fAQAAIAAJ 对我来说，它在严谨的数学论文和精彩的故事书之间找到了极佳的平衡点。

  There’s a very nice book about the Poincaré conjecture, going from the roots of geometry in Euclid’s Elements to Perelman’s proof: http://books.google.com/books?id=kM8fAQAAIAAJ At least for me it hit the sweet spot between a rigorous math paper and a good story book.

• hga · 2015 年

  ……里面有非常深刻的教训）。柏拉图和亚里士多德当然也值得关注！后者的《修辞学》（Rhetoric）内容，在你无法用辩证法说服别人的时候至关重要。欧几里得的《几何原本》（Euclid's Elements）在它所传授的知识领域里依然是天花板级别的。普鲁塔克很棒，但我实在太喜欢那段历史了。除此之外，我还建议读读李维（Livy）早期的一些著作。去读，或者更好的是……

  …very important object lessons in it). Surely Plato and Aristotle deserve some attention! The contents of the latter's Rhetoric is essential for when you can't reach people with dialectic. Euclid's Elements is still about as good as you can get for what it teaches. Plutarch is great, but I really like that period of history. To it I would add reading some of the earlier bits of Livy. Read, or better yet…

• anigbrowl · 2022 年

  ……弄不清该用哪种技巧，或者无法领会一个表面看起来复杂的东西其实很简单、只是表达得极度简炼。这些年我觉得值得一读的其他书：欧几里得的《几何原本》（Euclid's Elements），因为几何学得再扎实也不为过，而且里面的证明非常简洁，你可以当作热身练习；侯世达（Hofstadter）的《哥德尔、艾舍尔、巴赫：集异璧之大成》（GEB），它运用了幽默、诗歌、艺术……

  …sight of which techniques to reach for or appreciate how a superficially complex-looking thing is simple but being expressed very tersely. Other books I found worth reading over the years: Euclid's Elements, because you can't be too good at geometry and the proofs are so concise you can treat them as warm-up exercises Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid, which uses humor, poetry, art,…

• yottalove · 2021 年

  读完并理解欧几里得《几何原本》（Elements）的全部十三卷，最好是希腊语原文。这足以让你从根本上理解数学方法、它的威力以及应用——所有这一切仅仅源自少数几条公理和……

  Read and understand the thirteen books of the Elements by Euclid, preferably in the original Greek. This ought to be sufficient for a fundamental understanding of the mathematical method, its power and application--all generated from a handful of axioms and…

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