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Is this weird? Squaring Numbers.

  1. Aug 12, 2009 #1
    I'm 16, still in highschool. I consder myself pretty smart, but today I think I met one of the smarter people in my life.

    He's 14 and rides my bus. He scored ~10 points higher than me on a math test (i got 273, he got 285 I believe, not sure). I knew this, so I mentally ackknowledged that he was a little smarter than me. So, being quite the experimentalist, I ask him to square 27...nothing to big. He answers pretty easily, 729. So I ask him to square 191. He looks up and thinks about it, says a few numbers to himself, then says 36,641. I thought about it, and he was right.

    Now, I can square numbers like that pretty easily...but i've been pushing myself to that ability for a month or so now; I had to 'teach' myself little tricks to remember the numbers while computing. So I ask him if he had ever done that before, ever squared a number in the hundereds without a calculator. He says no? I was absolutely shocked! I cannot even come to comprehending that...to simply 'synthesize' how one would go about answering a problem like that, applying a method, then finding an answer in a matter of seconds..infact, he did it pretty easy. When I do it, i still feel pretty strained...but the thing is, no-one seems to understand why I'm so amazed by this! I mean, to just be able to do that so easily, he'd half to be like two or three times smarter than me...

    I have a tremendously easy time in math. I had a calculus class at my local university, and I was able to ace it without ever doing the work or paying attention in class, while I had 20 year olds scratching their heads...and this kid could be twice my mental ability? I can't comprehend how easy math must come to him.. He'll be opening calculus books and going,"well, duh" to things people twice his age struggle to learn. That is amazing! I feel like malcolm when he meets that eight year old with an IQ of 280 on Malcolm in the Middle...Im in absolute awe of this..please tell me someone understands?

    Oh and two things..sorry this is so irrelevant to the purpose of this forums..and sorry if I seem a tad pretentious. In actuallity, I'm really not that smart...early on I was very unorganized, so I never had a calculator. I think that has tremendously helped me in understand the relations of numbers.
  2. jcsd
  3. Aug 12, 2009 #2


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    Gold Member

    Why are you amazed? There's some simple tricks to multiplying two numbers together. It also doesn't mean you'll have a good comprehension of more advanced math.
  4. Aug 12, 2009 #3


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    Staff: Mentor

    Watch "Rain man" with Dustin Hoffman. Ability to calculate fast doesn't necesarilly come with what we consider smartness.
  5. Aug 12, 2009 #4
    It happens sometimes that one encounters people who are significantly more skilled at some task. Even in the professional world, coming across a true master at something is remarkable and humbling. This happens.

    The ability to mutiply two largish numbers is not too hard to do especially if one breaks it down piecemeal mentally. I suspect this is what your friend was doing. Not an extraordinary thing to do. Uncommon, but not extraordinary.

    I had a friend in college who was pursuing a degree in accounting. He could add, multiply, take percentages and divide largish numbers (including with fractional decimal components) with what seemed like ease. We used to challenge him with bizarre computational problems to see if he'd get it right. He usually did. However, he was lousy at integration and seriously did not enjoy higher math courses becuase they were so challenging.

    Even though I am an accomplished mathematician I cannot calculate mentally the way my friend did (I wish I could!). I would not take the fact that your friend was able to multiply two numbers quickly or that he got 10 more points than you did as evidence of being many time more intelligent. It is likely that he is bright is some ways, normal in others - just as you may be, but in different areas. Ask him how he does things - he may end up asking you for your methods when he runs into something that isn't quickly obtained.

    With that said, I've met (and been instructed by) some luminaries in their field and been awed by their accomplishments and the depth and sharpness of the their knowledge. That's quite an experience. It is always a learning opportunity.

  6. Aug 12, 2009 #5
    uhh....also he was wrong. 191 squared is 36,481 not 36,641. But had he been right (or maybe he was and that was a typo) then all the above posts are pretty much what I'd say.
  7. Aug 12, 2009 #6
    "Smart" is not graded on a linear scale. While it's convenient for teachers to rate every student from 0% to 100%, it's a very bad model for life in general.

    Even for two skills that seem related, there is no need for one person to be good at both. I graduated from college with a minor in mathematics. My friends are sometimes surprised when I have trouble multiplying two numbers both greater than 6. I'm very poor at mental math, but I really don't care. For the kind of math I like (which usually has a good visual or qualitative feeling), it doesn't have too strong of an impact on me.
  8. Aug 12, 2009 #7


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    Staff: Mentor

    Besides, it is not that hard:

    1912 = (200-9)2 = 2002 - 2*9*200 + 92
  9. Aug 12, 2009 #8
    A friend of mine is very talented in mental calculations, yet he's doing social sciences and says he's never enjoyed mathematics at all. I'd say the key to mental calculation is having an ordered line of thought and not getting interrupted, which are qualities my friend possesses to a high degree.

    Squaring is not hard at all once you get into it. Learn the squares from 1-30, the (a+-b)^2 rule and you can square all three digit numbers pretty easily.
  10. Aug 12, 2009 #9
    Or 191^2 = (191 + 9) * (191 - 9) + 9^2 = 200 * 182 + 81
  11. Aug 13, 2009 #10


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    Homework Helper

    I recently realized that I am most consistently the best in my grade/school at mentally adding, squaring, conversions from fractions to percentages/decimals and approximating square-roots.
    This, I believe, is due to my failure to be bothered to grab a calculator for every question asked. Whenever I can beat students to answering a question by mentally solving it while they spend time grabbing their calculators and punching in the numbers, it can be quite satisfying :biggrin:
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