Ask Tom: How to Find Measurements Without Math

[Seymore4Head]

[Don Y]

(sigh) Disappointing. He can't divide by 2? "evenly"

(Um, Tommy, every number can be divided -- by any other number -- "evenly"; it's just that the result may not be a nice convenient number for you to deal with!)

I just drilled a 2-7/8 hole offset 7-3/4 by 3-1/2 from a corner ("reference").

Center of 2-7/8 is:

one half of 2 -- let's call that 1!) once half of 7/8 -- let's call that 7/(8*2) = 7/16

Offset by 3-1/2 is 4.5+7/16 Offset by 7-3/4 is 8.75+7/16

You mean to tell me you can't find the "8.75" mark on a scale and count (on your fingers) seven more of the 1/16th markings??

I'm more interested in *real* tricks: e.g., find the center of a given circle!

[IGot2P]

Or even more interesting is to find the square root of -4. Any takers?

[Dan Espen]

Google.

Type in search:

square root -4.

Answer 2i.

Finding the center of a circle is just as easy.

[Paintedcow]

What kind of trees have Square Roots ? ? ?

[IGot2P]

If by chance someone does not know i = imaginary because there is no real number that is the square root of -4.

[Stormin Mormon]

The ones sawed down by lumber jacks with board feet?

[Mark Lloyd]

[snip]

And the other one?

One thing I remember from college is that EVERY number has TWO square roots. The other one is -2i. I even understand that.

Consider that when you find square roots, you halve the angle. For 4 (0 degrees = positive) roots are 2 (0 deg, 0+0=0) and -2 (180 deg,

180+180=0). For -4 ( 180 deg = negative) , roots are i2 (90 deg, 90+90=180) and -i2 (270 deg, 270+270=180).

Another thing, every number has 3 cube roots. However, that is more "complex". It took me about 30 years to understand that (including how that must be true). In case you care, polar representation makes more sense here, where the cube roots of 8 are 2 (0*3=0), 2@120 (120*3=0), and 2@240 (240*3=0).

Now, you can find the fourth roots of 16. Yes, there are 4 of them.

[Mark Lloyd]

[snip]

[Don Y]

[This space intentionally left blank?]

[Don Y]

Some of us (depends on your age and type of primary school education) learned how to "do square roots" by hand (sort of like "long division").

Do you realize that a similar process exists for "doing" cube roots?

[Mark Lloyd]

[snip]

I had a class in college where we would find square roots by hand.

[snip]