On Feb 25, 2024, sobriquet wrote on sci.math
(in article <urgojr$264hd$1@dont-email.me>):

>
> Suppose you want to simplify an expression and somehow Wolfram Alpha
> seems unable to do it for you. Are there any other ways to do it that
> can be relied on to yield an answer if there is one?
>
> For example consider this result:
>
> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>
> short alternative link:
>
> http://tinyurl.com/4ebtaedc
>
> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>
> Is there another way to get to that desired result when you're trying to
> simplify complicated expressions?
>
> Thx in advance for any feedback on this issue!

I forget my Mathematica and Maple now, but in one of them
you had to enclose the expression to be simplified in
Simplify( ) or Simplify[ ]. Then if that didn’t yield a
result you could try FullSimplify. And I am pretty sure
that Wolfram alpha uses the same syntax as Mathematica.
Maybe check out the help files for Simplify.

This thread started on sci.math but I have added
sci.math.symbolic . I would have added
comp.soft-sys.math.mathematica but it seems
that was abandoned by its moderators in 2014.

--
David Dalton dalton@nfld.com https://www.nfld.com/~dalton (home page)
https://www.nfld.com/~dalton/dtales.html Salmon on the Thorns (mystic page)
“And the cart is on a wheel; And the wheel is on a hill;
And the hill is shifting sand; And inside these laws we stand" (Ferron)

Op 26/02/2024 om 07:30 schreef David Dalton:
> On Feb 25, 2024, sobriquet wrote on sci.math
> (in article <urgojr$264hd$1@dont-email.me>):
>
>>
>> Suppose you want to simplify an expression and somehow Wolfram Alpha
>> seems unable to do it for you. Are there any other ways to do it that
>> can be relied on to yield an answer if there is one?
>>
>> For example consider this result:
>>
>> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
>> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
>> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
>> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>>
>> short alternative link:
>>
>> http://tinyurl.com/4ebtaedc
>>
>> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>>
>> Is there another way to get to that desired result when you're trying to
>> simplify complicated expressions?
>>
>> Thx in advance for any feedback on this issue!
>
> I forget my Mathematica and Maple now, but in one of them
> you had to enclose the expression to be simplified in
> Simplify( ) or Simplify[ ]. Then if that didn’t yield a
> result you could try FullSimplify. And I am pretty sure
> that Wolfram alpha uses the same syntax as Mathematica.
> Maybe check out the help files for Simplify.
>
> This thread started on sci.math but I have added
> sci.math.symbolic . I would have added
> comp.soft-sys.math.mathematica but it seems
> that was abandoned by its moderators in 2014.
>

It doesn't seem to yield the desired result in Mathematica (in the
Wolfram Cloud) or Wolfram Alpha:

https://i.imgur.com/npiwqPJ.png

https://www.wolframalpha.com/input?i=FullSimplify%5B%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%286%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bsqrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29%5D

David Dalton schrieb:
>
> On Feb 25, 2024, sobriquet wrote on sci.math
> (in article <urgojr$264hd$1@dont-email.me>):
>
> >
> > Suppose you want to simplify an expression and somehow Wolfram Alpha
> > seems unable to do it for you. Are there any other ways to do it
> > that can be relied on to yield an answer if there is one?
> >
> > For example consider this result:
> >
> > https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
> > 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
> > qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
> > 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
> >
> > short alternative link:
> >
> > http://tinyurl.com/4ebtaedc
> >
> > Why is Wolfram Alpha unable to see that this result is simply
> > sqrt(7)/8?
> >
> > Is there another way to get to that desired result when you're
> > trying to simplify complicated expressions?
> >
> > Thx in advance for any feedback on this issue!
>
> I forget my Mathematica and Maple now, but in one of them
> you had to enclose the expression to be simplified in
> Simplify( ) or Simplify[ ]. Then if that didn't yield a
> result you could try FullSimplify. And I am pretty sure
> that Wolfram alpha uses the same syntax as Mathematica.
> Maybe check out the help files for Simplify.
>
> This thread started on sci.math but I have added
> sci.math.symbolic . I would have added
> comp.soft-sys.math.mathematica but it seems
> that was abandoned by its moderators in 2014.
>

Assuming that "%CF%80" in the URL represents the imaginary unit #i,
your symbolic input expression reads:

1/SQRT(2)*SIN((1/8
- 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
+ SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
+ 82*SQRT(21/(7 + 4*SQRT(3)))))/#i)*2*pi)

in Derive notation.

I suspect that Alpha's atan() function ranges from -pi/2 to +pi/2 on
the real axis and usually should not be multiplied by 2*pi.

Numerical evaluation of my reading of your expression gives:

46.63320401 + 46.63052344*#i

whereas SQRT(7)/8 equals:

0.3307189137

Martin.

> Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> your symbolic input expression reads:

I haven't followed this thread closely, but that got me curious.
cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.

-JimC
--
James Cloos <cloos@jhcloos.com>
OpenPGP: https://jhcloos.com/0x997A9F17ED7DAEA6.asc

James Cloos schrieb:
>
> > Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> > your symbolic input expression reads:
>
> I haven't followed this thread closely, but that got me curious.
> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
>

Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed to
equal the ASCII string "pi" appearing a few characters later in the
URL. If the two are equal, the expression becomes:

1/SQRT(2)*SIN((1/8
- 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
+ SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
+ 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)

and evaluates numerically to:

-0.5445033022

which still does not equal SQRT(7)/8 though. Why should it?

Martin.

Op 26/02/2024 om 22:24 schreef clicliclic@freenet.de:
>
> David Dalton schrieb:
>>
>> On Feb 25, 2024, sobriquet wrote on sci.math
>> (in article <urgojr$264hd$1@dont-email.me>):
>>
>>>
>>> Suppose you want to simplify an expression and somehow Wolfram Alpha
>>> seems unable to do it for you. Are there any other ways to do it
>>> that can be relied on to yield an answer if there is one?
>>>
>>> For example consider this result:
>>>
>>> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
>>> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
>>> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
>>> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>>>
>>> short alternative link:
>>>
>>> http://tinyurl.com/4ebtaedc
>>>
>>> Why is Wolfram Alpha unable to see that this result is simply
>>> sqrt(7)/8?
>>>
>>> Is there another way to get to that desired result when you're
>>> trying to simplify complicated expressions?
>>>
>>> Thx in advance for any feedback on this issue!
>>
>> I forget my Mathematica and Maple now, but in one of them
>> you had to enclose the expression to be simplified in
>> Simplify( ) or Simplify[ ]. Then if that didn't yield a
>> result you could try FullSimplify. And I am pretty sure
>> that Wolfram alpha uses the same syntax as Mathematica.
>> Maybe check out the help files for Simplify.
>>
>> This thread started on sci.math but I have added
>> sci.math.symbolic . I would have added
>> comp.soft-sys.math.mathematica but it seems
>> that was abandoned by its moderators in 2014.
>>
>
> Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> your symbolic input expression reads:
>
> 1/SQRT(2)*SIN((1/8
> - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> + 82*SQRT(21/(7 + 4*SQRT(3)))))/#i)*2*pi)
>
> in Derive notation.
>
> I suspect that Alpha's atan() function ranges from -pi/2 to +pi/2 on
> the real axis and usually should not be multiplied by 2*pi.
>
> Numerical evaluation of my reading of your expression gives:
>
> 46.63320401 + 46.63052344*#i
>
> whereas SQRT(7)/8 equals:
>
> 0.3307189137
>
> Martin.

Here's what it looks like (screenshot) when I open the link in Wolfram
Alpha:

https://i.imgur.com/JwsKuic.png

"clicliclic@freenet.de" <nobody@nowhere.invalid> writes:

> James Cloos schrieb:
>>
>> > Assuming that "%CF%80" in the URL represents the imaginary unit #i,
>> > your symbolic input expression reads:
>>
>> I haven't followed this thread closely, but that got me curious.
>> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
>>
>
> Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed to
> equal the ASCII string "pi" appearing a few characters later in the
> URL. If the two are equal, the expression becomes:
>
> 1/SQRT(2)*SIN((1/8
> - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> + 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)
>
> and evaluates numerically to:
>
> -0.5445033022

If I take what the OP passed to Wolfram Alpha and add in the missing
operators I get this:

(1/sqrt(2))*sin((1/8-((6*(atan(1/4*(-20-12*sqrt(3))-sqrt(7*(7+4*sqrt(3)))+sqrt(102+58*sqrt(3)+142*sqrt(7/(7+4*sqrt(3)))+82*sqrt(21/(7+4*sqrt(3)))))))/pi))*2*pi)

Passing that to a calculator program I get:

~0.33071891388307382398

which is pretty close to SQRT(7)/8.

--
Ben.

Ben Bacarisse schrieb:
>
> "clicliclic@freenet.de" <nobody@nowhere.invalid> writes:
>
> > James Cloos schrieb:
> >>
> >> > Assuming that "%CF%80" in the URL represents the imaginary unit
> >> > #i, your symbolic input expression reads:
> >>
> >> I haven't followed this thread closely, but that got me curious.
> >> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
> >>
> >
> > Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed
> > to equal the ASCII string "pi" appearing a few characters later in
> > the URL. If the two are equal, the expression becomes:
> >
> > 1/SQRT(2)*SIN((1/8
> > - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> > + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> > + 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)
> >
> > and evaluates numerically to:
> >
> > -0.5445033022
>
> If I take what the OP passed to Wolfram Alpha and add in the missing
> operators I get this:
>
> (1/sqrt(2))*sin((1/8-((6*(atan(1/4*(-20-12*sqrt(3))-sqrt(7*(7+4*sqrt(3)))+sqrt(102+58*sqrt(3)+142*sqrt(7/(7+4*sqrt(3)))+82*sqrt(21/(7+4*sqrt(3)))))))/pi))*2*pi)
>
> Passing that to a calculator program I get:
>
> ~0.33071891388307382398
>
> which is pretty close to SQRT(7)/8.
>

Yes, that's because in my rendering of the original URL, I
misrepresented one of the denominators (7 + 4*SQRT(3)) as (7 + 4 +
SQRT(3)). With this mistake is corrected, I get 0.3307189137 as
required for SQRT(7)/8. Even better, Derive 6.10 now succeeds in
symbolically simplifying the trigonometric expression to SQRT(7)/8.

Case closed.

Martin.