Re: Obsolete Skills
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By the way, if anyone doesn't know the simple techniques for taking square roots and logarithms in your head, I can explain it if you're interested.
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That'd be cool.
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Taking really quite accurate square roots in your head is pretty easy. You have to know the perfect squars, but most people know those (I hope). Say you want the square root of 70. Obviously 8.x (greater than 8, less than 9). Take the difference between the number you want the square root of (70), subtract the next lowest perfect square (64), and divide by 2 times the whole number part of the square root (8). So the square root of 70 is 8+(70-64)/(2*8) = 8 6/16, or 8 3/8, which is accurate to one tenth of one percent. It also works the same for the next highest square, too, if that is closer. So the square root of 78 would be 9 - (81-78)/(2*9) = 9 - 3/18 = 9 - 1/6 = 8 5/6. Accurate to about 2 one-hundredths of one percent.
Any time you want to take a square root of a larger or smaller number, just extract an even numbered power of 10 and repeat. So the squart root of 4200 is the square root of 42 times ten, or about 65. Accurate to three tenths of one percent.
Base ten Logarithms require a small amount of memorization, but the pattern is not hard:
log(2) = 0.3
log(3) = 0.5
log(4) = 0.6
log(5) = 0.7
log(6) = 0.8
log(7) = 0.85
log(8) = 0.9
log(9) = 0.95
Since log(ab) = log(a) + log(b), you can take any large number, like 3x10^8, and its logarithm is easily calculable: log(3x10^8) = log(3)+log(10^8) = 8.5 (recall that log(10^n) = n). Accurate to three tenths of one percent.
If you need to take logarithms of numbers where the lead number is 1 (where the log function rises most steeply), you can do it like this. Say you need the log(120). log(120) = log(3*4*10) = 2.1 (to about 1%). This works for other numbers if you need more accuracy. Like log(35). Instead of turning that into log(3x10^1) or log(4x10^1), just make it log(5*7) = 0.7+0.85 = 1.55 (to about 0.4%)
You can also take sines, cosines and tangents pretty easily and accurately in your head, or use the binomial expansion to raise numbers near one to high powers easily. All sorts of mathematical tricks that are lost on most kids these days.
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WOW.
I am 48 and never learnt those.
We used log tables.
I bought myself my first calculator at the age of 17.
It cost me $60!
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