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> We start by finding a number that forms a perfect square that is close to 33 I usually just stop there which works for my use cases. :) > b=n/g. In practice

> We start by finding a number that forms a perfect square that is close to 33 I usually just stop there which works for my use cases. :) > b=n/g. In practice, computing b in your head may require an approximation I'm not sure how realistic this is to do in your head at all. Won't you introduce an error similar to the error of g anyway? Maybe "in your head" means without a calculator but on paper using long division.

nicoburns 4y ago
> Maybe "in your head" means without a calculator but on paper using long division. There's not really any benefit if you have paper available. But it's possible to do long division (and other "paper" techniques) in your head if your short-term memory is good enough.
- lcnPylGDnU4H9OF 4y ago
  > But it's possible to do long division (and other "paper" techniques) in your head if your short-term memory is good enough. That's actually how I learned long division. I didn't want to pay attention to any of these weird methods of arithmetic that require me to write things so I just did it all in my head and this happened to be a method that worked (go figure!). Many of my K12 math teachers understandably didn't like the fact that I would write down the correct answers to things without showing how I got there. On the topic of this article, I'm actually really glad for this trick. If anything is my hobby it is mental arithmetic.
- lurquer 4y ago
  Btw, doing long division in your head (during sex) is a good way to increase endurance…
  - wrycoder 4y ago
    Meanwhile, your partner says, “Beige. I’m going to paint the ceiling beige.”
    - lurquer 4y ago
      Exactly.
jethro_tell 4y ago
so, I don't know why this isn't brought up, but doing a lot of this kind of stuff in the field on construction sites, I'd have used 5 x 5 = 25 and 6 x 6 = 36 then split the difference so (36-25)/2 = 11/2 = 5.5, then you split the difference again in this process. For me, most estimation in the field is finding two known facts above and below and splitting the difference. Depending on your required precision, the above gets you pretty close right off the bat.
- deleted 4y ago
  [deleted]
- taneq 4y ago
  Yep, I use this for all sorts of things. Usually two known data points plus close-enough linear interpolation is accurate enough to estimate a value or sanity check a value you’ve been told.
- wrycoder 4y ago
  And that’s why the system of inches and fractions is better than it seems. Very easy to divide by two, which is a very common need.
  - jethro_tell 4y ago
    I mean, it's not easier than dividing in base 10. I've used both extensively and this is a really odd take.
    - wrycoder 4y ago
      Half of three and 5/8 inches: one and 5/16 plus 8/16: one and 13/16. Boom. That’s faster than dividing decimals in your head. It’s a useful system for residential construction, fast and accurate within about 0.031 inch. That kind of construction is done on four foot modules. Everything is marked right on the tape measure. The only time I use a calculator is to find the spacing to make an integral number of clapboards span a window. And, I have a construction calculator that works in feet, inches, and fractions, if I need to calculate stairs or something fancy. For cabinetmaking, either system is fine. For machining, I prefer metric, when the equipment can handle it. Otherwise, just use decimal inches, no feet, and keep your calculator handy.
MobiusHorizons 4y ago
I ended up using fractions in my head, which works pretty well as you essentially defer the division until the end. It’s a lot less state to carry in your head too. Basically you compute (n + g^2)/(2g) 33 + 36 = 69 2 * 6 = 12 69/12 = 5+ 9/12 = 5 + 3/4 = 5.75

nicoburns 4y ago

> Maybe "in your head" means without a calculator but on paper using long division. There's not really any benefit if you have paper available. But it's possible to do long division (and other "paper" techniques) in your head if your short-term memory is good enough.

lcnPylGDnU4H9OF 4y ago
> But it's possible to do long division (and other "paper" techniques) in your head if your short-term memory is good enough. That's actually how I learned long division. I didn't want to pay attention to any of these weird methods of arithmetic that require me to write things so I just did it all in my head and this happened to be a method that worked (go figure!). Many of my K12 math teachers understandably didn't like the fact that I would write down the correct answers to things without showing how I got there. On the topic of this article, I'm actually really glad for this trick. If anything is my hobby it is mental arithmetic.
lurquer 4y ago
Btw, doing long division in your head (during sex) is a good way to increase endurance…
- wrycoder 4y ago
  Meanwhile, your partner says, “Beige. I’m going to paint the ceiling beige.”
  - lurquer 4y ago
    Exactly.

jethro_tell 4y ago

so, I don't know why this isn't brought up, but doing a lot of this kind of stuff in the field on construction sites, I'd have used 5 x 5 = 25 and 6 x 6 = 36 then split the difference so (36-25)/2 = 11/2 = 5.5, then you split the difference again in this process. For me, most estimation in the field is finding two known facts above and below and splitting the difference. Depending on your required precision, the above gets you pretty close right off the bat.

deleted 4y ago
[deleted]
taneq 4y ago
Yep, I use this for all sorts of things. Usually two known data points plus close-enough linear interpolation is accurate enough to estimate a value or sanity check a value you’ve been told.
wrycoder 4y ago
And that’s why the system of inches and fractions is better than it seems. Very easy to divide by two, which is a very common need.
- jethro_tell 4y ago
  I mean, it's not easier than dividing in base 10. I've used both extensively and this is a really odd take.
  - wrycoder 4y ago
    Half of three and 5/8 inches: one and 5/16 plus 8/16: one and 13/16. Boom. That’s faster than dividing decimals in your head. It’s a useful system for residential construction, fast and accurate within about 0.031 inch. That kind of construction is done on four foot modules. Everything is marked right on the tape measure. The only time I use a calculator is to find the spacing to make an integral number of clapboards span a window. And, I have a construction calculator that works in feet, inches, and fractions, if I need to calculate stairs or something fancy. For cabinetmaking, either system is fine. For machining, I prefer metric, when the equipment can handle it. Otherwise, just use decimal inches, no feet, and keep your calculator handy.

MobiusHorizons 4y ago

I ended up using fractions in my head, which works pretty well as you essentially defer the division until the end. It’s a lot less state to carry in your head too. Basically you compute (n + g^2)/(2g) 33 + 36 = 69 2 * 6 = 12 69/12 = 5+ 9/12 = 5 + 3/4 = 5.75