Square root

[Farabi]

What is the difference between original squareroot with reciprocal squareroot?

[qWord]

squareroot  =  sqrt(x)
reciprocal squareroot = 1/sqrt(x)

::)

[dedndave]

sqr(2)/2 = 1/sqr(2)   :P

[Gunther]

Dave,

sqr(2)/2 = 1/sqr(2)   :P

that's a special case!

Gunther

[dedndave]

not too special
there are an infinite number of such cases   :P

[Vortex]

It's easy :

Code Select Expand

sqrt(x) / x = 1 / sqrt(x)

[Donkey]

Square root and reciprocal square root

[Gunther]

Hi Dave,

not too special
there are an infinite number of such cases   :P

my point was the division by 2. :lol:

Hi Vortex,

It's easy :

Code Select Expand

sqrt(x) / x = 1 / sqrt(x)

yes, of course.

Gunther

[Vortex]

Oops, an important statement is missing if we are in R3 :

Code Select Expand

sqrt(x) / x = 1 / sqrt(x)

with the condition :

Code Select Expand

x > 0

[qWord]

Oops, an important statement is missing if we are in R3 :

Code Select Expand

sqrt(x) / x = 1 / sqrt(x)

with the condition :

Code Select Expand

x > 0

also true for complex numbers.

[Vortex]

Off-topic : There are mental square root calculators with amazing capabilities. The art is to use cleverly the algorithms.

[FORTRANS]

Off-topic : There are mental square root calculators with amazing capabilities. The art is to use cleverly the algorithms.

Hi,

   Yeah, in high school there were two of us that could do
square roots on the fly.  For whatever reason, one semester
we were doing them.  I can't even find the procedure to do
it now.  (Rats.)  Or at least, the procedures I can find don't
seem to be usable with out paper and pencil.  (Hmm,  It was
while ago, late sixties.  Might be a clue?)

   Remember slide rules?  Log tables?

Cheers,

Steve N.

[dedndave]

it isn't hard
you deal with 2 input digits and one root digit at a time
then, basically a trial and error thing   :P
if the 2 digits are 20, you know the root digit is between 4 and 5 - use 4
then do the next 2 input digits

[KeepingRealBusy]

Off-topic : There are mental square root calculators with amazing capabilities. The art is to use cleverly the algorithms.

Hi,

   Yeah, in high school there were two of us that could do
square roots on the fly.  For whatever reason, one semester
we were doing them.  I can't even find the procedure to do
it now.  (Rats.)  Or at least, the procedures I can find don't
seem to be usable with out paper and pencil.  (Hmm,  It was
while ago, late sixties.  Might be a clue?)

   Remember slide rules?  Log tables?

Cheers,

Steve N.

I have the solution for you if you want it, along with several other methods I dreamed up and timed. I was doing the square root of BIG NUMS (up to 64 KB).

OBTW, the paper and pencil method came from a 1930's electronics text book my Dad had.

Dave.

[raymond]

I was doing the square root of BIG NUMS (up to 64 KB).

Curious to know which method you were using, binary or decimal with decimal input?