Secrets of mental math

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1. jyunwaiAug 2024
   This looks very cool, though it looks inconvenient for multiple problems due to the amount of drawing involved.

   A good, practical approach I've liked to use are the techniques in Benjamin and Shermer's "Secrets of Mental Math." One of the examples in the linked article shows a method of drawing for solving 42 * 21. But this is easier to solve mentally by converting this to a simpler problem, as recommended by the book: 42 * 21 = (42 * 20) + (42 * 1) = 840 + 42 = 882.

   You can often split up these types of multiplication problems into an easier multiplication problem, plus an addition. You can then solve the entire problem without much or any paper for calculation.

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2. mklApr 2023
   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.
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3. an_aparallelNov 2022
   to simplify what's wrong with mathematics education. I have been trying to go back and re-take so to speak, everything from basic algebra onwards. It struck me that my mental math chops were appalling. I've stumbled on a recommendation, here i think, of "Secrets of mental math" by Benjamin and Shermer...and goodness, as the book states several times - "why is this not taught in schools!"

   i mean, folks constantly say "when will i need this"...well, in my opinion, all the time...strikes me as odd that even folks I know who are decent at maths, cant do double, triple digit multiplications and the like in their heads. Beyond the math olympiad trickster outcomes you might get from this sort of study...having an intuition for COUNTING just seems so foundational to make sure you're...you know, not getting screwed over...in many areas.

   I also picked up an older popular mechanics "The Art of Mechanical Drawing" - by Willard, and within are some incredible drawings, of screws, nuts, bolts, sacred geometric patterns, celtic style crosses and so on. The ability to draw such things with set squares, compasses and so on is deemed an "obsolete skill"...but once again like counting...developing such a knack for this kind of drawing would be beyond handy for someone trying to diagram an idea they have, or even to explain things to others, or purely as a mental exercise of being able to manipulate shapes.

   Thirdly, take a look at the field of STEM - more popular than ever. But where are the incredibly detailed Mecanno, and Lego technics sets? Stores are filled with the shittiest looking banal "robots"

   I dont want to come across as tin-foil-hatted - however it just really seems that there is an active force at play to basically limit the strength of the average reasoning mind. I'm about 1/3 of the way through the above mental maths book. And once getting into it - i noticed a distinct increase and improvement in general focus in completely unrelated tasks. Once again, doubtful this is just some sort of coincidence.

   Maths - should be taught, as all subjects - in a transdisciplinary fashion. Engineering, Biology, Physics, Electronics, Computer Science - share so much common ground. Yet - we're still keeping them apart. We are still forcing people to choose 'one'... Sad.

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4. openknotFeb 2022
   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. I should recreate it.

   [0] Goodreads link: https://www.goodreads.com/book/show/83585.Secrets_of_Mental_...

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5. sitkackFeb 2022
   If the number you are calculating will be used as a lower bound, then rounding all the items up to the nearest 10s place and then using a little factoring can get one to the go/nogo solution.

   "can't be more than X"

   or

   "can't be less than Y"

   are powerful devices that allow one to keep thinking, rather than making tasks to be done later. But like the article mentions in the comments, if precision is warranted, then one needs to slow down and double check their work.

   As mentioned in the preface to Street Fighting Mathematics, "How to Solve It" by George Polya is another very approachable book. This tl;dr is pretty good [1] (aside, this book should be in the public domain by now)

   [1] https://math.ucr.edu/~res/math138A-2012/polya.pdf

   There are other books that train folks on how to do mental mathematics like

   * The Trachtenberg Speed System of Basic Mathematics https://www.abebooks.com/products/isbn/9780285629165/3011837...

   * Secrets of Mental Math https://www.abebooks.com/products/isbn/9780307338402

   I found this neat publication from the American Mathematical Society on Back of the Envelope calculation.

   https://www.ams.org/publications/TEXT-33-chap-1.pdf

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6. tzhenghaoNov 2017
   I highly recommend the Secrets of Mental Math book:

   http://a.co/095nXaa

   Lots of good insights on how to make shortcut mental calculations.

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