square root long division with 20 multiplier.

John E. Franklin · 2012-04-02 14:47:59

Remember the old Brittanica Encyclopedia from decades ago.
It contained a method to find square roots of numbers exactly
to however many digits you want. It used a 20 multiplier in
the process. It can be found on the internet with a little searching,
but I don't have a current link right at the moment. But anyway,
I was wondering, if you were in base-4, how could you alter the
algorithm so it would still work, and would you use a multiplier
of 8 or still 20. That I do not know. Anyone know of this?
Also any silly comments are also welcome as I love any information
that gives me ideas. Thanks a lot...

anonimnystefy · 2012-04-02 14:57:35

Hi JEF

Here you are:Square root by hand

And imagine if we counted in base 60.

Last edited by anonimnystefy (2012-04-02 15:16:44)

John E. Franklin · 2012-04-02 15:03:06

The link is funny so I fixed it:
http://www.homeschoolmath.net/teaching/square-root-algorithm.php

John E. Franklin · 2012-04-02 15:10:13

Hey that's awesome. That brings back a lot of memories of reading that when I was little.
Nice example. So the 20 is actually a doubling and then you add one more digit (chiffre).
Thnks for da link, though it had http-http twice in a row so it failed, but anyway, it's not
your fault, there is a glitch in the system it seems, so i reposted. But this is really awesome.
I think I will finally remember it for a long time, especially if I use it a few times on paper
tomorrow.

anonimnystefy · 2012-04-02 15:10:25

Hi JEF

On another site I found that that same algorithm works in other bases as well,but it probably uses multiplication in that system.

John E. Franklin · 2012-04-02 15:13:09

Sweet, thanks for the encouraging word on the algorithm holding over bases. I will experiment sometime in the next month when I feel the urge to learn it more. I think I will make a times table in base-4 and an adding table in base-4 to help me out in the hand calculations.

anonimnystefy · 2012-04-02 15:15:41

Hi JEF

Nice,but what about base 60?

anonimnystefy · 2012-04-02 15:17:21

I also fixed the link!

John E. Franklin · 2012-04-02 15:21:12

Hmmm, base-60, wow, I think I could put the numbers in parethesis instead of using 26 upper/lower case = 52 + 8 numbers.
I think I could just do (45) (46)... (59), (01)(00),(01)(01), for the writing system.
But as for the times table, it could be printed out with a simple little BASIC program I guess, but do you recommend base-60 first, over base-4 for some reason. Will it be more fun or something?

anonimnystefy · 2012-04-02 15:24:02

Hi JEF

You said to post ideas. You make of it what you want now.

Btw,some ancient civilizations used the base 60 numeral system and that's why we count an hour like 60 seconds and stuff.

John E. Franklin · 2012-04-02 15:25:16

Oh, yeah, I've heard of the Samarians or some people with a similar name that did the 60 thing.
Did you know the 12 on the clock may have come from Egyptians counting knuckles on one hand?

anonimnystefy · 2012-04-02 15:28:33

No but that's an interesting fact.

Btw there are some algorithms for cube rooting numbers as well. Just thought you might want to know.

John E. Franklin · 2012-04-02 15:31:01

Hmmm.... cube roots, that's an interesting thought. Now fifth roots would be next since 4th roots are just square roots twice, so then after that I guess 7th roots would be next to learn since the cube root and square root sequence is probably the sixth root, is that right, or is it 2x3 or 2+3?

John E. Franklin · 2012-04-02 15:35:09

Yeah, I think you just need the prime number root algorithms really.
Because 65536 or 2**16 or 2^16 when square rooted 4 times on the calculator goes down to 2,
via 256, 16, 4, 2, so that kind of points to 2*2*2*2=16, so
hence
cube root follwoed by another cube root would be 3x3=9th root.

anonimnystefy · 2012-04-02 15:35:15

Yup,sixth root=cube root(square root).

John E. Franklin · 2012-04-02 15:38:34

Yeah, that's what I just kind of saw with the intermittant post #14 seconds before yours.

anonimnystefy · 2012-04-02 15:41:35

I know,I was just confirming.

John E. Franklin · 2012-04-02 15:42:01

I've heard prime numbers are good for little more than encryption, but now this might be a new one for people to work on, including myself I guess. I bet it will be a tough going project to get to the higher prime roots, could take years of trial and error. But first I'll have to see the various cube root algorithms, and then see if anyone has higher prime ones on the net.

anonimnystefy · 2012-04-02 16:02:37

Hi jeff

Maybe we can design our own algorithm for prime roots.

John E. Franklin · 2012-04-02 16:08:40

Yeah, I've been reading lots of stuff on the net about a cube root algorithm,
and then i was reading about a smart guy who can find 13th roots in his head in a speed contest,
but his methods are not revealed, and he is not doing the decimal parts, he is only doing ones
that come out to natural numbers for the answer, but starting with 200 digit long numbers.
Amazing, but not really on the subject because he is probably doing a lot of narrowing down by
multiplying quickly in his head and readjusting until he gets the answer, but still, whatever his
method, the article didn't say.

Math Is Fun Forum

#1 2012-04-02 14:47:59

square root long division with 20 multiplier.

#2 2012-04-02 14:57:35

Re: square root long division with 20 multiplier.

#3 2012-04-02 15:03:06

Re: square root long division with 20 multiplier.

#4 2012-04-02 15:10:13

Re: square root long division with 20 multiplier.

#5 2012-04-02 15:10:25

Re: square root long division with 20 multiplier.

#6 2012-04-02 15:13:09

Re: square root long division with 20 multiplier.

#7 2012-04-02 15:15:41

Re: square root long division with 20 multiplier.

#8 2012-04-02 15:17:21

Re: square root long division with 20 multiplier.

#9 2012-04-02 15:21:12

Re: square root long division with 20 multiplier.

#10 2012-04-02 15:24:02

Re: square root long division with 20 multiplier.

#11 2012-04-02 15:25:16

Re: square root long division with 20 multiplier.

#12 2012-04-02 15:28:33

Re: square root long division with 20 multiplier.

#13 2012-04-02 15:31:01

Re: square root long division with 20 multiplier.

#14 2012-04-02 15:35:09

Re: square root long division with 20 multiplier.

#15 2012-04-02 15:35:15

Re: square root long division with 20 multiplier.

#16 2012-04-02 15:38:34

Re: square root long division with 20 multiplier.

#17 2012-04-02 15:41:35

Re: square root long division with 20 multiplier.

#18 2012-04-02 15:42:01

Re: square root long division with 20 multiplier.

#19 2012-04-02 16:02:37

Re: square root long division with 20 multiplier.

#20 2012-04-02 16:08:40

Re: square root long division with 20 multiplier.

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