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%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


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!

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XPost: sci.math.symbolic

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)

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XPost: sci.math.symbolic

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

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XPost: sci.math.symbolic

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.

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XPost: sci.math.symbolic

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

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XPost: sci.math.symbolic

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.

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XPost: sci.math.symbolic

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

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XPost: sci.math.symbolic

"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.

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XPost: sci.math.symbolic

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.

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Op 26/02/2024 om 02:13 schreef sobriquet:

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%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

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 guess one option would be to enter the pattern in the continued
fraction to see if that yields a simplified answer.

https://www.wolframalpha.com/input?i=continued+fraction+%5B0%3B+3%2C%7B42%2C6%7D%5D

continued fraction [0; 3,{42,6}]

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