Metric vs. other measurement systems - chart

[FEM2008]

I was taught that awkward system in grade school. I soon purged it from my memory bank. There's a much simpler way to find roots using Newton's method.

Consider this iterative equation...

x2 = (x1 + N / x1) / 2

where:

N = number whose root is to be found
x1 = initial estimate of root
x2 = improved estimate of root

We make a guess of the root, x1, plug it into this equation and get an improved estimate, x2. If this estimate isn't good enough for out purposes, we set x1 = x2 and repeat the process to get an even better estimate. This iterative procedure is repeated until x2 squared is close enough to N to satisfy our requirements.

@mklotz . BTW. I brought this up recently and my son informed me this is Babylonian method, not Newtonian. I looked ut up. This method is also known as Heron's method. His detailed deccription goes back to 60 AD.

[mklotz]

@mklotz . BTW. I brought this up recently and my son informed me this is Babylonian method, not Newtonian. I looked ut up. This method is also known as Heron's method. His detailed deccription goes back to 60 AD.

The derivation of Newton's method is generally done by using the definition of a derivative. Since Newton (and Leibniz) developed calculus the method probably came to be known by Newton's name.

The Babylonians and Heron had nothing like calculus so it's not clear how they stumbled upon the iteration. My guess was by trying various numerical methods or by numerically extending something that works without iteration for perfect squares.

Example:

Let 'n' be the square root of 'N'. Then N/n = n and (n + N/n) = 2 * n so:

n = (n + N/n) / 2

It's not a huge intellectual leap to think that, if n is close to the square root, then the result of the above calculation should produce a number closer to the true root, iow an iterator...

n2 = (n1 + N/n1) / 2

[MeJasonT]

holy crap, the worlds round - when were you going to tell me. Next you will say Pluto isnt a planet.

In the famous song title by Jellybean - im just visiting this planet

I missed the Apollo bus coming back from the moon so i had to wait for the next one, nobody said it ws the last bloody bus.

[Frank S]

When it comes to drill bits I prefer two size numerations well possibly a 3rd
Imperial decimal for smaller or critical sizes higher end millimeter grades since those you can buy in tenths of a MM from the tiny through as large as you want, and lastly a fractional set in 64ths You can forget those 1,2,3s and A,B,C sizes I have no use for them although I do have a set of both

[hemmjo]

snip.... You can forget those 1,2,3s and A,B,C sizes I have no use for them although I do have a set of both

I think we need to be careful here. I have no use for lots of things that others find useful, but that is no reason to forget them or dismiss their usefulness for others.

It is the, "I have no use for ....." mentality that makes some people (especially legislators) think that "if I don't need it, no one needs it".

I would have hoped that this discussion would have help us be more open with our thoughts.