心算的秘密
Secrets of mental math
Arthur Benjamin · 初版 2006 年
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为什么值得读
- 适合初学者快速建立心算与代数思维联系
- 显著提升应对复杂问题的费米估算能力
- 解析从高位起算顺应阅读习惯的心算技巧
这些简单的数学秘诀和小技巧将彻底改变你看待数字世界的方式。《Secrets of Mental Math》将让你迅速像数学天才一样思考。准备好用你从未想过自己能掌握的神奇计算技能去惊艳你的朋友——以及你自己吧！著名“数学魔术师”Arthur Benjamin 在书中分享了他实现闪电般快速心算以及惊艳数字戏法的秘诀技巧。本书将教会你在脑海中以远超想象的速度进行计算，大幅提升你对数字的记忆力，并且——或许是人生头一次——让数学变得趣味横生。是的，
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接着看他那本稍微进阶一点的《The Art of Insight in Science and Engineering》[0]。我觉得这两本书加上 Art Benjamin 的《Secrets of Mental Math》[1]，能把你的费米估算（Fermi calculation）能力提升到另一个段位。[0] https://mitpress.mit.edu/books/art-insight-science-and-engin...
Follow that up with his slightly more advanced The Art of Insight in Science and Engineering [0]. I feel like these two books plus Art Benjamin's Secrets of Mental Math [1] would put your Fermi calculation abilities on another level. [0] https://mitpress.mit.edu/books/art-insight-science-and-engin...
……当没有现成的漂亮公式让你直接套用时，该如何应对难题。我们每周都会用这本书里的方法死磕一道难题。4. 我还没把它排进进度，但 Arthur Benjamin 的《Secrets of Mental Math》里有很多干货，能在日后把算术思维和代数思维扎实地连接起来。
…hard problems when you're not handed a nice formula to plug things into. Once a week, we work through a hard problem using the method in this book. 4. I haven't worked it in yet, but Arthur Benjamin's "Secrets of Mental Math" has a lot of stuff in it that will solidly connect arithmetic and algebraic thinking later.
关于这个主题有两本绝佳的书：Arthur Benjamin 的《Secrets of Mental Math》（适合初学者）和 Ronald Doerfler 的《Dead Reckoning: Calculating Without Instruments》（更进阶）。Mind Your Decisions 博客（http://mindyourdecisions.com/blog/tag/mental-math/）……
Two excellent books on the subject are Secrets of Mental Math by Arthur Benjamin (for beginners) and Dead Reckoning: Calculating Without Instruments by Ronald Doerfler (more advanced). The Mind Your Decisions blog (http://mindyourdecisions.com/blog/tag/mental-math/)…
值得一读：我妻子大学教授之一 Arthur Benjamin 写的《Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks》。
Worth a read: "Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks" by Arthur Benjamin, one of my wife's college professors.
根本没人颠倒它，这就是我的核心观点。大家现在用的数字顺序，正是最适合从左到右（LTR）阅读语言心算的顺序——最高位数字排在最前面。可以参考 Arthur Benjamin 的《Secrets of Mental Math》一书。它也是 LTR 语言中最适合快速估算出大致量级的方式。这是因为大家都在用的数字顺序本来就是针对 LTR 语言设计的。
No one switched it around, that's my point. The digit order everyone uses is the one best suited to mental arithmetic in LTR languages, where the most significant digit is first. See the book Secrets of Mental Math by Arthur Benjamin. It's also the best suited to getting a rough idea of the number quickly in LTR languages. That's because the digit order everyone uses was designed for LTR languages.
讲这个的一本好书是 Benjamin 和 Shermer 写的《Secrets of Mental Math》[0]。我记得很多年前把那些速算技巧背下来时觉得特别好玩，但可惜后来把复习用的电子抽认卡（flash card）卡组弄丢了，所以现在全忘光了。……
A great book for this is "Secrets of Mental Math" by Benjamin and Shermer [0]. I remember a feeling of fun when I memorized the tricks many years ago, but unfortunately I lost the digital flash card deck for reviewing them, so I've forgotten them now.…