calculating 3+ root with only a square root function
Marc Adler
only has a square root function (like the HP12C)?
I'm surprised to find out that the HP12C, the ogosho of financial
calculators, doesn't have this function, since to calculate a growth
rate (of, say, earnings per share), you divide the first and last
values and then take the nth root of the result, n being the number of
periods (say, years) in between.
Ex:
2002 2001 2000 1999
$1.41 $1.27 $1.05 $0.87
1.41/0.87 = 1.62
Third root (because 2002-1999 = 3) of 1.62 = 0.18 = 18% growth rate
This is pretty fundamental, so why can't the HP12C do it? Is there a
workaround?
TIA,
Marc
pi
alain verghote
I know several ways to compute x^(1/n) with sqrt(x).
I propose an approach by a 2^p power ,p integer:
Example 1) y =x^(1/3) -> y^3= x
or y^4 = x*y so y=sqrt(sqrt(x*y));
we therefore have an iterative formula
y(i+1)=sqrt(sqrt(x*y(i)) , try with y=5^(1/3)
starting with y0=1 come on ...
Example 2) y^17=20 -> y^16=20/y gives
y(i+1)=sqrt(sqrt(sqrt(sqrt(20/y(i)) ;
or y(i+1)=sqrt^[4](20/y(i)) ;[] iterations ,
try with y0=1
You still need a stop rule for 1) and 2) ,
Good luck,Alain.
W. Dale Hall
Does the calculator have natural logarithm and exponential functions?
That would surely do the trick:
x^(1/n) = exp(log(x)/n)
Dale.
--
Dale.
Dirk Van de moortel
"W. Dale Hall" <mailto...@pacbell.net> wrote in message news:2t7de.11468$J12....@newssvr14.news.prodigy.com...
The calculator has y^x:
http://www.hpmuseum.org/12c.jpg
That will do the trick as well :-)
Dirk Vdm
Marc Adler
Thanks,
Marc
Arturo Magidin
If you want to find the cubic root of y, take y^{1/3} (i.e., x=1/3).
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
mag...@math.berkeley.edu
Oscar Lanzi III
can do is square roots, the following method will work.
1) Start with the binary representation of 1/(the root index), which
you must compute beforehand. Thus, for example, for a 5th root you have
0.001100110011... .
2) Let n be your number. Define R = 1 and S = sqrt(n).
3) If the first digit in the binary representation is 0, do nothing.
If the digit is 1, multily R by S and define the product as your new
value of R.
4) Take the square root of S and define that as your new value of S.
5) If |s-1| is less than the maximum relative error you will tolerate,
multiply R by s and take that as your approximate root. The actual root
is sure to be between R and R*S^2. Otherwise repeat (3) and (4) with
each digit of the binary representaiton, in order.
6) Once you have figured out how tedious this is, get a calculator that
has the additional functions others have recommended.
--OL
José Carlos Santos
> How can y^x be used to find the root?
y^(1/3) is the cube root of y.
Best regards,
Jose Carlos Santos
N. Silver
> How can y^x be used to find the root?
To find the cube root of 8, we use these keys:
8 [y^x] (1/3) [=].
The root always is in the bottom. For example,
the fifth root of 32 is 32 to the 1/5th power.
Dirk Van de moortel
"Marc Adler" <marc....@gmail.com> wrote in message news:1114972672.8...@z14g2000cwz.googlegroups.com...
> How can y^x be used to find the root?
For example for the cube root of 20:
20
Enter
3
1/x
y^x
Enjoy!
Dirk Vdm
Marc Adler
Anyone know why the HP12C doesn't have this function? Also, as to
buying a scientific calculator, I have one, but the HP12C has built-in
functions for calculating loans, bonds, depreciation, and other things.
Marc
G. A. Edgar
Back in the Olden Days, when we used slide rules, some slide rules had
a K scale for cubes and cube roots. But others didn't. One slide rule
manual I remember had instructions for finding cube roots using only
the ABCD scales. It was interesting for me to figure out why it
worked!
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
Dirk Van de moortel
"Marc Adler" <marc....@gmail.com> wrote in message news:1114974697....@f14g2000cwb.googlegroups.com...
> Great! Thanks a lot!
>
> Anyone know why the HP12C doesn't have this function?
Simply because it is implemented with the y^x function.
As far as I know, no calculator has a built-in cube root. They
almost all have a square root, thanks to Pythagoras, so to
speak :-)
> Also, as to
> buying a scientific calculator, I have one, but the HP12C has built-in
> functions for calculating loans, bonds, depreciation, and other things.
So it seems... and as from now it has a cube root as well :-)
Dirk Vdm
N. Silver
> Anyone know why the HP12C doesn't have this function?
Because it's a specialized calculator from the last century?
> Also, as to buying a scientific calculator, I have one,
Yours is obsolete.
> but the HP12C has built-in functions for calculating loans,
> bonds, depreciation, and other things.
There newer machines with all the capibilities you need
"rolled into one." And if they do not, they can be modified
with a download or by writing short programs.
JEMebius
Marc Adler wrote:
because it is intended for people on a different planet, where genuine mathematics is unknown.
Johan E. Mebius
P.S.: Finance children and directors: please do not be hurt.
Randy Poe
> Is it possible to calculate an nth root where n>2 on a calculator
that
> only has a square root function (like the HP12C)?
>
I don't see y^x or x^y listed as one of the built-in functions
on HP's website for the 12C.
However they do have e^x and ln(x), so here's how to do the
n-th root with logs:
cuberoot(x) = e^(ln(x)/n)
Enter number.
Take ln(x).
Divide by n
Take e^x.
- Randy
Arturo Magidin
Randy Poe <poespa...@yahoo.com> wrote:
>Marc Adler wrote:
>> Is it possible to calculate an nth root where n>2 on a calculator
>that
>> only has a square root function (like the HP12C)?
>>
>
>I don't see y^x or x^y listed as one of the built-in functions
>on HP's website for the 12C.
>
>However they do have e^x and ln(x), so here's how to do the
>n-th root with logs:
>
>cuberoot(x) = e^(ln(x)/n)
Should be "n-th root"
>Enter number.
>Take ln(x).
>Divide by n
>Take e^x.
Dirk Van de moortel
"Randy Poe" <poespa...@yahoo.com> wrote in message news:1115063983.0...@g14g2000cwa.googlegroups.com...
> Marc Adler wrote:
> > Is it possible to calculate an nth root where n>2 on a calculator
> that
> > only has a square root function (like the HP12C)?
> >
>
> I don't see y^x or x^y listed as one of the built-in functions
> on HP's website for the 12C.
You don't see it on
http://www.hpmuseum.org/12c.jpg
?
Really?
Dirk Vdm
Virgil
wrote:
Doesn't the HP12C have logarithmic and anti-logarithmic functions?
If so, the numerate (mathematically literate) can still do powers and
roots.
Randy Poe
Dirk Van de moortel wrote:
> "Randy Poe" <poespa...@yahoo.com> wrote in message
news:1115063983.0...@g14g2000cwa.googlegroups.com...
> > Marc Adler wrote:
> > > Is it possible to calculate an nth root where n>2 on a calculator
> > that
> > > only has a square root function (like the HP12C)?
> > >
> >
> > I don't see y^x or x^y listed as one of the built-in functions
> > on HP's website for the 12C.
>
> You don't see it on
> http://www.hpmuseum.org/12c.jpg
No, I didn't see it here:
http://www.hp.com/calculators/financial/12c/
which is HP's page for a 12C calculator you can order
today.
Statistical/Mathematical Features:
* Cumulative statistical analysis
* Std. deviation, mean, weighted mean
* Linear regression
* Forecasting, correlation coefficient
* Total, ∑x, ∑x2, ∑y, ∑y2, ∑xy
* +, -, x, %, ÷, 1/x, ±, LN, e^x, n!
But come to think of it, they don't even list square root
on that list.
So as I said, I don't see it LISTED on any of the product
description pages at hp.com. I still don't.
However, I did find this just now:
"How do I... Calculate the 4th and 5th roor of a number?"
HP 12c
To calculate the 4th root of 81:
1. Press 81, then ENTER
2. Press 4, [1/x], then [y^x]
3. Answer = 3"
So obviously there is a y^x key. They just don't mention it
in their "great mix of mathmatical and scientific functions".
> > cuberoot(x) = e^(ln(x)/n)
Note obvious typo. I started to describe cube root, changed
it to a description of n-th root, and forgot to edit the
left hand side.
- Randy
JEMebius
picture of the HP12C at http://www.hpmuseum.org/12c.jpg - there is on
the A21 place a y^x function key.
Unfortunately there is no y^(1/x) key, nor has the HP11C such a function
key. At both models the 1/x key is directly to the right of y^x, so
HP12C users - financial people - can handle exponential and power
functions as easily as scientific and technical people. My prank is
partly unjustified.
So for the cubic root of X one enters X, presses ENTER, enters 3,
presses 1/x and y^x and reads off the answer.
The HP12C has logarithmic and anti-logarithmic functions as well.
Ciao - Johan E. Mebius
Dirk Van de moortel
"Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote in message
news:O8xde.79684$2W7.5...@phobos.telenet-ops.be...
>
> "Randy Poe" <poespa...@yahoo.com> wrote in message news:1115063983.0...@g14g2000cwa.googlegroups.com...
> > Marc Adler wrote:
> > > Is it possible to calculate an nth root where n>2 on a calculator
> > that
> > > only has a square root function (like the HP12C)?
> > >
> >
> > I don't see y^x or x^y listed as one of the built-in functions
> > on HP's website for the 12C.
>
> You don't see it on
> http://www.hpmuseum.org/12c.jpg
> ?
> Really?
[reply to Randy's reply - which is impossible without my
reformatting the who message and inserting quoting characters]
Indeed, they don't mention
y^x, sqrt(x), Frac, Intg and a few more.
< ;-) >
They don't even mention the fact that they forgot to
implement the "=" key, so I'll have a word with them.
</ ;-) >
Dirk Vdm
Dirk Van de moortel
"JEMebius" <jeme...@xs4all.nl> wrote in message news:4276CD58...@xs4all.nl...
> After I wrote my prank on financially-oriented people I hit upon a
> picture of the HP12C at http://www.hpmuseum.org/12c.jpg - there is on
> the A21 place a y^x function key.
>
> Unfortunately there is no y^(1/x) key, nor has the HP11C such a function
> key. At both models the 1/x key is directly to the right of y^x, so
> HP12C users - financial people - can handle exponential and power
> functions as easily as scientific and technical people. My prank is
> partly unjustified.
> So for the cubic root of X one enters X, presses ENTER, enters 3,
> presses 1/x and y^x and reads off the answer.
>
> The HP12C has logarithmic and anti-logarithmic functions as well.
>
> Ciao - Johan E. Mebius
Don't you read the other replies before you repeat the
same thing that 4 people already replied? ;-)
Dirk Vdm
JEMebius
thoughtless reactions.
Johan E. Mebius
Dirk Van de moortel wrote: