yeah, jeff, tell us.

Jeff,

Out of curiosity, what in the world would you use Quad Root for?

Ole Thom

At this point I could claim that I was just the programmer, not the engineer.
And, in fact, it was specifically my job to implement scientific libraries, both
at the Observatory where I worked and in the software I sold. It was also done
at Lotus, but by then I was wise enough to not get involved. Newton's
approximation is used quite often in many areas - it not only does simple roots,
but also general roots of polynomial functions. I used it in one of the last
major programs I wrote - a charting program based 3D animation techniques (you
could spin the pie chart like a top, or do "fly throughs" of 3D bar charts).
The reason the skills I learned on "primitive" computers were still in demand is
that we slow down our modern machines with pigs like Java, yet the customer
demands real-time, 3D response!

Although we don't think about "fourth roots" in day to day life, its easy to
find an example relevant to sailing: The return echo strength from Radar is
proportional to the fourth root of the distance.


"Thom Stewart" wrote in message
...
Jeff,

Out of curiosity, what in the world would you use Quad Root for?

Ole Thom

Thom, it is obvious jeffies doesn't have a clew.

4th roots are used in electronic design engineering, for one. Other areas for
sure but none come to mind off the top of my head. My career was spent
explaining high tech to executives, not designing the stuff.

At this point I could claim that I was just the programmer, not the engineer.
And, in fact, it was specifically my job to implement scientific libraries,
both
at the Observatory where I worked and in the software I sold. It was also
done
at Lotus, but by then I was wise enough to not get involved. Newton's
approximation is used quite often in many areas - it not only does simple
roots,
but also general roots of polynomial functions. I used it in one of the last
major programs I wrote - a charting program based 3D animation techniques
(you
could spin the pie chart like a top, or do "fly throughs" of 3D bar charts).
The reason the skills I learned on "primitive" computers were still in demand
is
that we slow down our modern machines with pigs like Java, yet the customer
demands real-time, 3D response!

Although we don't think about "fourth roots" in day to day life, its easy to
find an example relevant to sailing: The return echo strength from Radar is
proportional to the fourth root of the distance.


"Thom Stewart" wrote in message
...
Jeff,

Out of curiosity, what in the world would you use Quad Root for?

Ole Thom

thom, a side story about calc'ing 2nd roots.

once upon a time, way back when an electronic calculator cost more than 3 times
the price of a brand VW bug, and mechanical calcs cost about 140% of the price
of a VW, a group of us (National Science Foundation Summer Students) were shown
just how fantastic an expensive mechanical calc was.

(note, mechanical calc could add, subtract, multiply [slow] and divide [slow to
really slow, depending the numbers involved] out to about 18 digits.
Electronic calc's [made only by Friden as I recall] could do the same, plus
"hold" two additional numbers in a "stack". No calculators of the time had
printed output.)

The college instructor started working through the process involved to
calculate a square root using the process jeffies outlined. After he had been
working and calculating and working for maybe 5 minutes, I and another guy
started working the problem by hand. While the instructor had 20 digits to
work with in short order, his accuracy was only about two digits. In fact his
accuracy using the machine never did keep up on a digit by digit basis with us
working the problem by hand.

btw, most people who needed to do nth roots as part of their jobs all
personally owned a table of logs. If you will willing to pay the price, I
believe you could get tables out to 12 digits or more. Usually that kind of
accuracy was not needed.