From Newsgroup: sci.math

[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.math

On Sun, 28 Dec 2025 04:27:13 +0100, Thomas 'PointedEars' Lahn wrote:

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

It's already been solved, but for the record:

1:

(8*sqrt(3)*cos(t)*sqrt(3*cos(t)^2+1)*sin(t)+(27*cos(t)^4+18*cos(t)^2+3)*sin(t))/(36*cos(t)^4+24*cos(t)^2+4)

2:

(sqrt(3*cos(t)^2+1)*(9*cos(t)^2+3)*sin(t)+8*sqrt(3)*cos(t)*sin(t))/(sqrt(3*cos(t)^2+1)*(12*cos(t)^2+4))



However, you may want to attempt these. Again, they
are both equal and one should be reducible to the other:

1:

-((sqrt(3)*sin(t)^2*sqrt(4-3*sin(t)^2))/(9*cos(t)^4+6*cos(t)^2+1))

2:

(sqrt(3)*cos(t)^2-sqrt(3))/(3*cos(t)^2+1)^(3/2)
--
Gentoo: the only road to GNU/Linux freedom and perfection.
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From Newsgroup: sci.math

On Sun, 28 Dec 2025 04:27:13 +0100, Thomas 'PointedEars' Lahn wrote:

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.

You are probably one of the very few individuals that has that opinion.
Most others hold the opposite view.

ASCII is already long dead and buried. Unicode is now the medium
for text communication and it specifically includes many pages, or
blocks, of math symbols.

Usenet is fully Unicode capable and there is no valid reason to
exclude Unicode math expressions.

Consider the following integral:

integrate(x/sqrt(a*x+b),x)

The output in ASCII is very ugly and inefficient:

+-------+
(2 a x - 4 b)\|a x + b
-----------------------
2
3 a

However, with Unicode the output is very nicely formed:

_________
ro#ro#a ria x + b ria (2 ria a ria x - 4 ria b) roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
2
3 ria a


These are simple expressions and one can imagine how much worse ASCII
would appear for very complicated expressions.

Unicode is the only way to go.

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

There should be a way to stop that, but I don't use ThB.
--
Gentoo: the only road to GNU/Linux freedom and perfection.
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From Newsgroup: sci.math

On Sun, 28 Dec 2025 13:48:25 +0000, Farley Flud wrote:

ASCII is already long dead and buried. Unicode is now the medium
for text communication and it specifically includes many pages, or
blocks, of math symbols.

Here's another example:

integrate(1/(a*x^2+b*x+c),x)

The ugly ASCII response:

+----------+
| 2 +----------+
(2 a x + b)\|4 a c - b 2 | 2
- 2 b atan(------------------------) + log(a x + b x + c)\|4 a c - b
2
4 a c - b
-----------------------------------------------------------------------]
+----------+
| 2
2 a\|4 a c - b



The very pleasing Unicode response (differently simplified):

rAc 2 ria a ria x + b rAR
b ria atan rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL ______________rAf
rAc 2 rAR rAL ro# 2rAf
log rAYa ria x + b ria x + crAa rAYro#ro# 4 ria a ria c - b rAa roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC - roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
2 ria a ______________
ro# 2
a ria ro#ro# 4 ria a ria c - b



The Unicode is far better for communication.
--
Gentoo: the only road to GNU/Linux freedom and perfection.
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From Newsgroup: sci.math

Farley Flud wrote:
^^^^^^^^^^^
Socially, your *real* name belongs there. And technically, an actual
*e-mail address* belongs in the From header field value, too. See RFC 5536.

On Sun, 28 Dec 2025 04:27:13 +0100, Thomas 'PointedEars' Lahn wrote:

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.

You are probably one of the very few individuals that has that opinion.
Most others hold the opposite view.

ASCII is already long dead and buried. Unicode is now the medium
for text communication and it specifically includes many pages, or
blocks, of math symbols.

You are missing the point.

1. I wrote: Unicode *art*. My recommendation was that you do not post
ASCII or Unicode *drawings*, but use plain text, for equations.

2. You can use Unicode *characters* (if you had paid more attention,
you would have seen that I am doing that myself) as long as you are
aware that not all fonts that people use contain all Unicode
characters. Notably, Google's Noto fonts (which are supposed to
have *fewer* gaps) contain *less* mathematical symbols (at least for
use under Windows 10; it may be different under other OSes) than e.g.
the Quivira font.

3. You can use either Unicode or ASCII characters as long as you are
aware that some newsreaders have reserved some of those to allow
for minimal text formatting. For example, text enclosed in

4. There is no need to use Unicode when newsreaders are able to convert
common sequences like x^2 for display to the corresponding Unicode
characters *anyway*.

5. Arguably, it is more tedious to type mathematical Unicode characters
(although I have designed an Xkb keyboard layout for that, and I am
working on a LaTeX-to-Unicode converter) than ASCII/Windows-1252
characters, although equations using the latter can be more difficult
to read. It depends on the terms and the audience.

Usenet is fully Unicode capable

Network News is; that is a difference. In the German-speaking Usenet we
have a saying: Internet is the thing with cables; Usenet is the thing with *people*.

and there is no valid reason to exclude Unicode math expressions.

You are wrong; there is. In particular, there are several valid and good reasons to not post equations as *drawings*.
--
PointedEars

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

Farley Flud wrote:
^^^^^^^^^^^
Socially, your *real* name belongs there. And technically, an actual
*e-mail address* belongs in the From header field value, too. See RFC 5536.

On Sun, 28 Dec 2025 04:27:13 +0100, Thomas 'PointedEars' Lahn wrote:

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.

You are probably one of the very few individuals that has that opinion.
Most others hold the opposite view.

ASCII is already long dead and buried. Unicode is now the medium
for text communication and it specifically includes many pages, or
blocks, of math symbols.

You are missing the point.

1. I wrote: Unicode *art*. My recommendation was that you do not post
ASCII or Unicode *drawings*, but use plain text, for equations.

2. You can use Unicode *characters* (if you had paid more attention,
you would have seen that I am doing that myself) as long as you are
aware that not all fonts that people use contain all Unicode
characters. Notably, Google's Noto fonts (which are supposed to
have *fewer* gaps) contain *less* mathematical symbols (at least for
use under Windows 10; it may be different under other OSes) than e.g.
the Quivira font.

3. You *can* use either Unicode or ASCII characters as long as you are
aware that some newsreaders have reserved some of those to allow
for minimal text formatting. For example, words enclosed in underscores
are displayed underlined, words enclosed in asterisks are displayed in
bold, and words enclosed in slashes are displayed italic, by Thunderbird.
The corresponding delimiters are then *removed* from display, which makes
especially your ASCII/Unicode *drawings* of equations ambiguous (e.g., if
you write a superscript as a character in the line above, one cannot be
certain -- without additional work -- what it is the superscript/exponent
of).

4. There is no need to use Unicode when newsreaders are able to convert
common sequences like x^2 for display to the corresponding Unicode
characters *anyway*.

5. Arguably, it is more tedious to type mathematical/physical Unicode
characters (although some years ago I have designed an Xkb keyboard
layout for that, and I am working on a LaTeX-to-Unicode converter)
than ASCII/Windows-1252 characters, although equations using the latter
can be more difficult to read. It depends on the terms and the audience.

Usenet is fully Unicode capable

Network News is; that is a difference. In the German-speaking Usenet we
have a saying: Internet is the thing with cables; Usenet is the thing with *people*.

and there is no valid reason to exclude Unicode math expressions.

You are wrong; there is. In particular, there are several valid and good reasons to not post equations as *drawings*.
--
PointedEars

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

Farley Flud wrote:

On Sun, 28 Dec 2025 13:48:25 +0000, Farley Flud wrote:

ASCII is already long dead and buried. Unicode is now the medium
for text communication and it specifically includes many pages, or
blocks, of math symbols.

Here's another example:

integrate(1/(a*x^2+b*x+c),x)

The ugly ASCII response:

+----------+
| 2 +----------+
(2 a x + b)\|4 a c - b 2 | 2
- 2 b atan(------------------------) + log(a x + b x + c)\|4 a c - b
2
4 a c - b
-----------------------------------------------------------------------]
+----------+
| 2
2 a\|4 a c - b

The very pleasing Unicode response (differently simplified):

rAc 2 ria a ria x + b rAR
b ria atan rALroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCrAf
rAL ______________rAf
rAc 2 rAR rAL ro# 2rAf
log rAYa ria x + b ria x + crAa rAYro#ro# 4 ria a ria c - b rAa roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC - roCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroCroC
2 ria a ______________
ro# 2
a ria ro#ro# 4 ria a ria c - b

Sigh. [psf 10.1]

<https://photos.app.goo.gl/JiCdbAEU5M1ypjtKA>

Do you understand now?

The Unicode is far better for communication.

[It is _Unicode_, not "the Unicode".]

If only you used it as it was intended to be used.
--
PointedEars

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

Thomas 'PointedEars' Lahn wrote:

3. You *can* use either Unicode or ASCII characters as long as you are
aware that some newsreaders have reserved some of those to allow
for minimal text formatting. For example, words enclosed in underscores
are displayed underlined, words enclosed in asterisks are displayed in
bold, and words enclosed in slashes are displayed italic, by Thunderbird.
The corresponding delimiters are then *removed* from display, which makes
especially your ASCII/Unicode *drawings* of equations ambiguous (e.g., if
you write a superscript as a character in the line above, one cannot be
certain -- without additional work -- what it is the superscript/exponent
of).

Correction: Thunderbird does not remove the delimiters for display.
However, I noticed that sometimes this interpretation interferes with ASCII
art (as I am an ASCII artist myself :))

The reason why your drawings are displayed distorted appears to be instead
(I noticed that in my own equations, too, especially when Unicode-only characters preceded ASCII characters, such as an implies symbol preceded the rest of an equation) that there is insufficient support by common monospace fonts (or newsreaders, at least Mozilla Thunderbird) for characters that can only be found in Unicode, such as the left top part of an opening
parenthesis: they are displayed, but not given the same width as other characters (I tried Consolas -- this was the default and used in the photo
that I shared -- and Noto Sans Mono; Quivira would be optimal regarding character coverage, but it is not a monospace font; DejaVu Sans Mono has the spacing right most of the time, and your drawings so far look OK in my Thunderbird.) But the correct display of ASCII/Unicode art requires that
*all* characters have the same width.

In any case, it is less efficient to discuss mathematics your (current) way,
so I would still recommend to not *draw* *formulas*. (I find nothing problematic with making ASCII art, and in a limited way even Unicode art, to illustrate a concept; on the contrary.)
--
PointedEars

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

On Mon, 29 Dec 2025 00:49:14 +0100, Thomas 'PointedEars' Lahn wrote:

<https://photos.app.goo.gl/JiCdbAEU5M1ypjtKA>

Do you understand now?

It looks fine in my Pan newsreader.

Usenet text messaged should be displayed "as is" using monospaced fonts.
By "as is" I mean that the newsreader should not render any characters or character combinations in some special fashion.

Unicode was designed to facilitate math communication using plain text
format and it does so admirably.
--
Hail Linux! Hail FOSS! Hail Stallman!
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From Newsgroup: sci.math

Farley Flud wrote:

On Mon, 29 Dec 2025 00:49:14 +0100, Thomas 'PointedEars' Lahn wrote:

<https://photos.app.goo.gl/JiCdbAEU5M1ypjtKA>

Do you understand now?

It looks fine in my Pan newsreader.

In German we have an adage which roughly translates to "The worm has to be tasty to the fish, not the fisherman."

A corresponding well-known network adage is: "Be conservative in what you
send, be liberal in what you accept from others."

IOW: Do you want your postings to be *read* (by as many people as possible)?
Then you should post in a manner that is *easy* to read (by *most* people).
Do you want to *discuss* mathematics? Then you should present your mathematics in a way that is *easy* to discuss.

I am pretty sure that somewhere in the charter of this newsgroup there are
also recommendations if not requirements how mathematical formulas should be posted, and I am pretty sure that ASCII/Unicode *art* is NOT among them as, display issues aside, it is very inefficient to discuss mathematics this way.

Usenet text messaged should be displayed "as is" using monospaced fonts.

As I already told you: This *was* viewed with a monospace font, Consolas (by Microsoft; I do not know whether I chose it -- it works well in programming
-- or whether it is the default monospace font in Windows 10).

DejaVu Sans Mono appears to work better in that regard, but it also contains less mathematical symbols, and the display of your drawings is still not perfect.

By "as is" I mean that the newsreader should not render any characters or character combinations in some special fashion.

Given that the *vast* majority of people are using Mozilla-based
applications to participate in Usenet, including this newsgroup, nowadays,
you are pretty much alone with that opinion:

$ awk '/^User-Agent:/ { sub("^User-Agent:[[:space:]]*", ""); ua[$0] += 1; }
END { for (key in ua) print(ua[key], "\t", key); }' sci.math | sort -nr
1892 Mozilla Thunderbird
56 Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101
30 slrn/pre1.0.4-9 (Linux)
6 tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64))
6 Pan/0.146 (Hic habitat felicitas; d7a48b4
4 Mozilla/5.0 (Windows NT 6.1; Win64; x64; rv:128.0) Gecko/20100101 Firefox/128.0
4 Mozilla/5.0 (Windows NT 6.1; Win64; x64; rv:128.0) Gecko/20100101
2 slrn/1.0.3 (Linux)
2 Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
2 Mozilla/5.0 (Macintosh; Intel Mac OS X 10.9; rv:32.0)
Gecko/20100101 Firefox/32.0 SeaMonkey/2.29.1
2 Hogwasher/5.24
2 Gnus/5.13 (Gnus v5.13)
2 ForteAgent/8.00.32.1272
1 Pan/0.146 (Hic habitat felicitas; d7a48b4 gitlab.gnome.org/GNOME/pan.git)
1 Mozilla/5.0 (Windows NT 6.1; WOW64; rv:128.0) Gecko/20100101

Unicode was designed to facilitate math communication using plain text
format and it does so admirably.

Unicode was NOT designed so that you use its (block) characters to *draw* mathematics; but it contains a lot of characters so that you can *write* mathematics:

<https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode>

So you SHOULD just do that. (Also because you keep violating network
standards -- .linux is not a registered TLD, so it cannot be part of an
e-mail address as required by RFC 5536 --: EOD for me.)
--
PointedEars

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

On 12/29/2025 06:07 PM, Thomas 'PointedEars' Lahn wrote:

<https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode>

So you SHOULD just do that. (Also because you keep violating network standards -- .linux is not a registered TLD, so it cannot be part of an e-mail address as required by RFC 5536 --: EOD for me.)

Email addresses ending with ".invalid" are valid invalid e-mail
addresses, ..., the charter though suggests that posters should
use a real e-mail address.


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