From Newsgroup: sci.physics

Any math heads out there?

The following two expressions are equal. That is, substituting any value
of t in the expressions will produce the same value.

Yet, I cannot reduce one to the other using algebra and the trig identities.
It must be possible but I can't find a way to do it.

Can you?

Eternal fame awaits the person who can solve this.


Expression 1:

rAc _______________ rAR
rAL _ ro# 2 rAc 4 2 rAR rAf
rAL8 ria ro#ro#3 ria cos(t) ria ro#ro# 3 ria cos(t) + 1 ria sin(t) + rAY27 ria cos(t) + 18 ria cos(t) + 3rAa ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL 4 2 rAf
rAY 36 ria cos(t) + 24 ria cos(t) + 4 rAa


Expression 2:

rAc _______________ rAR
rAL ro# 2 rAc 2 rAR _ rAf
rALro#ro# 3 ria cos(t) + 1 ria rAY9 ria cos(t) + 3rAa ria sin(t) + 8 ria ro#ro#3 ria cos(t) ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL _______________ rAf
rAL ro# 2 rAc 2 rAR rAf
rAY ro#ro# 3 ria cos(t) + 1 ria rAY12 ria cos(t) + 4rAa rAa
--
Gentoo: the only road to GNU/Linux freedom and perfection.
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From Newsgroup: sci.physics

On Wed, 24 Dec 2025 13:30:01 +0000, Farley Flud wrote:

Any math heads out there?

Eternal fame awaits the person who can solve this.

You may be wondering how I arrived at these particular expressions
and what they have to do with GNU/Linux.

Fret not. I shall reveal.

I was exploring general tangent plane vectors along a general
sphere geodesic using the open-source GNU/Linux Maxima:

<https://maxima.sourceforge.io/>

I had derived the covariant derivative of the general tangent
vector using both the intrinsic (Christoffel symbols) and extrinsic
(projection onto unit normal) methods. They should be equal
but the expressions were different. Yet they are indeed equal.
One must be reducible to the other but I can't figure out how
to do it.

If you can perform this reduction you will gain everlasting
fame.

So get to it.
--
Gentoo: the only road to GNU/Linux freedom and perfection.
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From Newsgroup: sci.physics

[pointless Followup-To comp.os.linux.advocacy ignored; F'up2 sci.math set]

Farley Flud wrote:

Any math heads out there?

The following two expressions are equal. That is, substituting any value
of t in the expressions will produce the same value.

Yet, I cannot reduce one to the other using algebra and the trig identities. It must be possible but I can't find a way to do it.

Can you?

Next time, use standard (ASCII) notation and not Unicode *art*. There is a place and time for ASCII and Unicode art; posting mathematical problems on Usenet is NOT it.

Notice that at least Thunderbird converts some ASCII character sequences to Unicode, like x^2 (x followed by circumflex followed by 2).

Before I attempt to simplify this: Are the expressions below those that you meant?

Eternal fame awaits the person who can solve this.

8-)

Expression 1: [rewritten using standard notation as I see it]

{8 sqrt(3) cos(t) sqrt[3 cos^2(t) + 1] sin(t)
+ [27 cos^4(t) + 18 cos^2(t) + 3] sin(t)}/
{36 cos^4(t) + 24 cos^2(t) + 4}

Expression 2: [ditto]
[...]

{sqrt[3 cos^2(t) + 1] [9 cos^2(t) + 3] sin(t) + 8 sqrt(3) cos(t) sin(t)}/ {sqrt[3 cos^2(t) + 1] [12 cos^2(t) + 4]}

--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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From Newsgroup: sci.physics

On 12/24/25 7:30 AM, Farley Flud wrote:

Any math heads out there?

The following two expressions are equal. That is, substituting any value
of t in the expressions will produce the same value.

Yet, I cannot reduce one to the other using algebra and the trig identities. It must be possible but I can't find a way to do it.

Can you?

Eternal fame awaits the person who can solve this.

Expression 1:

rAc _______________ rAR
rAL _ ro# 2 rAc 4 2 rAR rAf
rAL8 ria ro#ro#3 ria cos(t) ria ro#ro# 3 ria cos(t) + 1 ria sin(t) + rAY27 ria cos(t) + 18 ria cos(t) + 3rAa ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL 4 2 rAf
rAY 36 ria cos(t) + 24 ria cos(t) + 4 rAa

Expression 2:

rAc _______________ rAR
rAL ro# 2 rAc 2 rAR _ rAf
rALro#ro# 3 ria cos(t) + 1 ria rAY9 ria cos(t) + 3rAa ria sin(t) + 8 ria ro#ro#3 ria cos(t) ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL _______________ rAf
rAL ro# 2 rAc 2 rAR rAf
rAY ro#ro# 3 ria cos(t) + 1 ria rAY12 ria cos(t) + 4rAa rAa

They're equal. Place the two expressions on either sides of an equal
sign. Factor out and get rid of sin(t). Then do the following substitution:

a = square root of (3cost^2 +1)

Both sides will quickly reduce to the same result in terms of a.


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From Newsgroup: sci.physics

On 2026-01-04, Physfitfreak <physfitfreak@gmail.com> wrote:

On 12/24/25 7:30 AM, Farley Flud wrote:

Any math heads out there?

The following two expressions are equal. That is, substituting any value
of t in the expressions will produce the same value.

Yet, I cannot reduce one to the other using algebra and the trig identities. >> It must be possible but I can't find a way to do it.

Can you?

Eternal fame awaits the person who can solve this.


Expression 1:

rAc _______________ rAR
rAL _ ro# 2 rAc 4 2 rAR rAf
rAL8 ria ro#ro#3 ria cos(t) ria ro#ro# 3 ria cos(t) + 1 ria sin(t) + rAY27 ria cos(t) + 18 ria cos(t) + 3rAa ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL 4 2 rAf
rAY 36 ria cos(t) + 24 ria cos(t) + 4 rAa


Expression 2:

rAc _______________ rAR
rAL ro# 2 rAc 2 rAR _ rAf
rALro#ro# 3 ria cos(t) + 1 ria rAY9 ria cos(t) + 3rAa ria sin(t) + 8 ria ro#ro#3 ria cos(t) ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL _______________ rAf
rAL ro# 2 rAc 2 rAR rAf
rAY ro#ro# 3 ria cos(t) + 1 ria rAY12 ria cos(t) + 4rAa rAa

They're equal. Place the two expressions on either sides of an equal
sign. Factor out and get rid of sin(t). Then do the following substitution:

a = square root of (3cost^2 +1)

Both sides will quickly reduce to the same result in terms of a.

Correct.

Factor.
Simplify the fraction
Factor once more.
Simplify the fraction again.

Both expressions are equal.

Easy peasy.
--
pothead

rCLLiberals seem to assume that, if you donrCOt believe in their particular political solutions, then you donrCOt really care about
the people that they claim to want to help.rCY

rCo Thomas Sowell
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From Newsgroup: sci.physics

On 2026-01-03 21:17, pothead wrote:

On 2026-01-04, Physfitfreak <physfitfreak@gmail.com> wrote:

On 12/24/25 7:30 AM, Farley Flud wrote:

Any math heads out there?

The following two expressions are equal. That is, substituting any value >>> of t in the expressions will produce the same value.

Yet, I cannot reduce one to the other using algebra and the trig identities.
It must be possible but I can't find a way to do it.

Can you?

Eternal fame awaits the person who can solve this.


Expression 1:

rAc _______________ rAR
rAL _ ro# 2 rAc 4 2 rAR rAf
rAL8 ria ro#ro#3 ria cos(t) ria ro#ro# 3 ria cos(t) + 1 ria sin(t) + rAY27 ria cos(t) + 18 ria cos(t) + 3rAa ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL 4 2 rAf
rAY 36 ria cos(t) + 24 ria cos(t) + 4 rAa


Expression 2:

rAc _______________ rAR
rAL ro# 2 rAc 2 rAR _ rAf
rALro#ro# 3 ria cos(t) + 1 ria rAY9 ria cos(t) + 3rAa ria sin(t) + 8 ria ro#ro#3 ria cos(t) ria sin(t)rAf
rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL _______________ rAf
rAL ro# 2 rAc 2 rAR rAf
rAY ro#ro# 3 ria cos(t) + 1 ria rAY12 ria cos(t) + 4rAa rAa

They're equal. Place the two expressions on either sides of an equal
sign. Factor out and get rid of sin(t). Then do the following substitution: >>
a = square root of (3cost^2 +1)

Both sides will quickly reduce to the same result in terms of a.

Correct.

Factor.
Simplify the fraction
Factor once more.
Simplify the fraction again.

Both expressions are equal.

Easy peasy.

Man, how I wish I could still do math.
--
CrudeSausage
John 14:6
Pop_OS!
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From Newsgroup: sci.physics

On Sat, 3 Jan 2026 20:06:06 -0600, Physfitfreak wrote:

They're equal. Place the two expressions on either sides of an equal
sign. Factor out and get rid of sin(t). Then do the following substitution:

a = square root of (3cost^2 +1)

Yes. Now try the following. Both expressions are equal. Reduce one
to the other:

1)

rAc _______________rAR
rAL _ 2 ro# 2rAf
rALro#ro#3 ria sin(t) ria ro#ro# 4 - 3 ria sin(t) rAf -rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL 4 2 rAf
rAY 9 ria cos(t) + 6 ria cos(t) + 1 rAa



2)

_ 2 _
ro#ro#3 ria cos(t) - ro#ro#3 roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
rAc3rAR
rALroCrAf
rAY2rAa
rAc 2 rAR
rAY3 ria cos(t) + 1rAa



Again, these are another component of the 2 vectors produced by
Maxima. The vectors are equal but Maxima has simplified each
differently. But Maxima cannot reduce one to the other, at least
not with the default procedures.
--
Gentoo: the only road to GNU/Linux freedom and perfection.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.physics

On Sun, 04 Jan 2026 11:20:03 +0000, Farley Flud wrote:

2)

_ 2 _
ro#ro#3 ria cos(t) - ro#ro#3 roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
rAc3rAR
rALroCrAf
rAY2rAa
rAc 2 rAR
rAY3 ria cos(t) + 1rAa

For some reason, #2 did not print properly. The numerator should
be:

sqrt(3) * cos(t)^2 - sqrt(3)
--
Gentoo: the only road to GNU/Linux freedom and perfection.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.physics

CrudeSausage <crude@sausa.ge> amok-crossposted in comp.os.linux.advocacy and sci.physics:

[full quote]

Man, how I wish I could still do math.

I wish that one would need something like a driver's license before one
would be allowed to post to Usenet, and that that could be revoked or
suspended if one failed to use it properly on a regular basis -- like
violating foreign namespaces with "funny" "addresses", bothering other newsgroups with off-topic amok-crossposts, and full-quoting.

F'up2 poster
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
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From Newsgroup: sci.physics

Farley Flud amok-crossposted to comp.os.linux.advocacy and sci.physics again:

For some reason, #2 did not print properly. The numerator should
be:

sqrt(3) * cos(t)^2 - sqrt(3)

Nobody *here* cares about that. FOAD.
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.physics

On 1/4/26 9:04 AM, Thomas 'PointedEars' Lahn wrote:

CrudeSausage <crude@sausa.ge> amok-crossposted in comp.os.linux.advocacy and sci.physics:

Man, how I wish I could still do math.

I wish that one would need something like a driver's license before one
would be allowed to post to Usenet, and that that could be revoked or suspended if one failed to use it properly on a regular basis -- like violating foreign namespaces with "funny" "addresses", bothering other newsgroups with off-topic amok-crossposts, and full-quoting.

F'up2 poster

Oh we're *so* surprised, some geekwad from sci.physics crossposts a
reply to bitch about crossposting, adding to the issue as he talks about having a license to post, full of his esoteric rules he would dictate to everyone. You should really lose your virginity.
--
Joel W. Crump
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From Newsgroup: sci.physics

On 1/4/26 5:31 AM, Farley Flud wrote:

On Sun, 04 Jan 2026 11:20:03 +0000, Farley Flud wrote:

2)

_ 2 _
ro#ro#3 ria cos(t) - ro#ro#3
roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
rAc3rAR
rALroCrAf
rAY2rAa
rAc 2 rAR
rAY3 ria cos(t) + 1rAa

For some reason, #2 did not print properly. The numerator should
be:

sqrt(3) * cos(t)^2 - sqrt(3)

On my screen it is properly printed.

Uploaded any of those videos of yours recently? :)
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From Newsgroup: sci.physics

Physfitfreak crossposted to comp.os.linux.advocacy and sci.physics without Followup-To:

On 1/4/26 5:31 AM, Farley Flud wrote:

On Sun, 04 Jan 2026 11:20:03 +0000, Farley Flud wrote:

2)

_ 2 _
ro#ro#3 ria cos(t) - ro#ro#3
roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
rAc3rAR
rALroCrAf
rAY2rAa
rAc 2 rAR
rAY3 ria cos(t) + 1rAa

For some reason, #2 did not print properly. The numerator should
be:

sqrt(3) * cos(t)^2 - sqrt(3)

On my screen it is properly printed.

To me the term looks like

[reU(3) cos(t)^2 - reU(3)]/[3 cos^(t)^2 + 1]^(3/2),

but only if I use DejaVu Sans Mono 13pt (not, for example, with Consolas
12pt, another monospace font).

So this is more evidence that it is not a good idea (that should even
convince the staunchest supporter) to *draw* equations (using Unicode) in Usenet. [As you can see, I can find nothing wrong with *writing* Unicode characters when using ASCII would be clumsy instead.]

F'up2 sci.math
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
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From Newsgroup: sci.physics

On 12/24/25 7:30 AM, Farley Flud wrote:

Any math heads out there?

This one befits a math head better:

An Iranian Ayatollah invites a penniless Iranian scientist to give him a visit. When the scientist visits him, he goes like:

Ayatollah: We gave this question to every engineer we could and none of
them could answer it. Fat, thin, short, tall, rich, or super rich,
didn't matter. None of those donkeys could answer it. Then someone said
why not asking a scientist, so now you're here.

Scientist: What is the question?

Ayatollah: I have gathered fund to distribute a large number of spies throughout occupied Palestine (Israel.) All of them are non-Iranian, and
have different ethnicity. We have divided up the entire land into as
many zones as we plan to assign spies to. The spies will only contact
each other if they're stationed in neighboring zones. But we do not want
any spy have a neighboring spy of the same ethnicity.

Scientist: !.. Why not?

Ayatollah: Because if of the same ethnicity, their stupid wives will be talking each other's brains on the phone all day and Mossad can easily
get suspicious of the two households.

Scientist: Oh!..

Ayatollah: So here's the problem we have. We prefer to use as few
different ethnicity among the spies as possible. So what is the minimum
number of different ethnicity we can limit our process to, to distribute
them in a way to prevent any neighboring spies of same ethnicity?

And he continues:

Ayatollah: So are we done here?

Scientist: Of course not. What's in it for me? I'm not one of your 5
million Basij slave to do it free for you.

Ayatollah: Hmm.. how about ... much in advance and another ... much
after you come up with the answer?

The scientist takes out his smartphone and uses the astronomical number
to convert the amount into U.S. dollar, and then:

Scientist: Holy fucking shit.. I'm in it!

So he gets the first payment and goes home, works on the problem for a
day, and goes back and gives the answer to the Ayatollah and gets the
final payment.

What was his answer?




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From Newsgroup: sci.physics

Four, of course.
--
John Hasler
john@sugarbit.com
Dancing Horse Hill
Elmwood, WI USA
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From Newsgroup: sci.physics

On 1/6/26 10:16 PM, John Hasler wrote:

Four, of course.

:-)



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