On Wed, 20 May 2026 07:29:06 +0200, fir wrote:
i wonder if it would be not good in programing and on cpu level
having a type for angles
it seem ofr sure ot should be form 0.00 to 0.9999999.. so its kinda
float
Radians are the most natural unit for most trig calculations.
<https://gitlab.com/ldo/python_topics_notebooks/-/blob/master/Angle%20Units.ipynb?ref_type=heads>
On Wed, 20 May 2026 10:03:20 +0200, fir wrote:
Lawrence D?Oliveiro pisze:
i dont know in fact but i dont think so - imo 0...1 has more sense
Radians are the most natural unit for most trig calculations.
In radians,
sin x ? x as x ? 0
But only in radians.
fir pisze:
Summary:
For the whole software ecosystem:
essentially negligible.
For phase-heavy kernels:
potentially very noticeable.
For DSP/audio/simulation:
a genuinely meaningful idea.
Historically:
it could have been quite powerful.
Mathematically:
it is a very elegant concept.
Architecturally:
the problem is too niche for mainstream x64 ISA support.
sorry for talkin with ai (i uset to talk with myself (its a joke, i was
not talking with myself really just adding thoughts) so now i can talk
withm myself and ai ;c but as this group is not big and in some topic is
not a biger chance for indepth discussion i can post some ai answers
which in turn trigges many f smaller potential points of dicussion if
someone is interested (and if no may skip/ignore..still for me most
important is if subject is good and thoughts are reasonable)
radians suck (and should be thrown out both c and math)
On Fri, 22 May 2026 15:20:08 -0700, Chris M. Thomasson wrote:
I use radians all the damn time!
Radians are the most natural units for most trig calculations.
But I have no problem with supporting different angle units. Let the
user input angles in whatever units they want, and get back answers in whatever units they want. Internally, all angles get converted to
radians, the calculations are done, and the results converted back
again.
What annoys me just a bit is seeing these little functions like
?degrees to radians? and ?radians to degrees? -- so you need two
conversion functions (converting to and from radians) for every angle
unit you want to support.
It?s simpler to just offer a single conversion factor, which can be
used like this:
®angle-in-units-X¯ ? ®conversion-factor-for-units-X¯ ? ®angle-in-radians¯
and going the other way:
®angle-in-radians¯ ö ®conversion-factor-for-units-X¯ ? ®angle-in-units-X¯
So for example if you want angles in degrees, then the conversion
factor is ã/180; if you want to work in units of full circles, then
the conversion factor is 2ã. All nice and simple, and scalable, too.
On Sun, 24 May 2026 15:57:38 +0800, makendo wrote:
(Irrational numbers are discovered around 2,500 years ago.)
The Pythagoreans were horrified by the discovery. They saw it as some
kind of defect in the perfection of mathematics, and therefore of
reality, itself.
They tried to cover it up. One story is that the mathematician
Hippasus was killed to keep him from revealing the secret.
On Wed, 20 May 2026 10:03:20 +0200, fir wrote:
Lawrence D?Oliveiro pisze:
i dont know in fact but i dont think so - imo 0...1 has more sense
Radians are the most natural unit for most trig calculations.
In radians,
sin x ? x as x ? 0
But only in radians.
On 21/05/2026 02:23, Lawrence D?Oliveiro wrote:...
In radians,
sin x ? x as x ? 0
But only in radians.
actually sinx -> x as x -> 0
and that's true of any linear function of x defined close to x=0, so
also for degrees and grads.
ITYM "sin x is approximately = x for small x" which is only gesturally
useful because it doesn't say /how/ approximate for /how/ small - in
which we find that we can use degrees as long as we multiply our approximation threshold when we divide our size threshold.
On 2026-06-11 23:47, Tristan Wibberley wrote:
On 21/05/2026 02:23, Lawrence D?Oliveiro wrote:...
In radians,
sin x ? x as x ? 0
But only in radians.
actually sinx -> x as x -> 0
and that's true of any linear function of x defined close to x=0, so
also for degrees and grads.
ITYM "sin x is approximately = x for small x" which is only gesturally
useful because it doesn't say /how/ approximate for /how/ small - in
which we find that we can use degrees as long as we multiply our
approximation threshold when we divide our size threshold.
sin x = x - x^3/3! + ... is true only when x is in radians. cos x = 1 = x^2/2! + ... is also true only in radians. There's similar expansions
for all of the trig functions, and radians are favored by those
forumulas because they are simplest in those units.
sin x = (e^{ix} - e^(-ix))/2, and the similar formulas for the other
trig functions get more complicated when x is in radians.
On 21/05/2026 22:16, fir wrote:
fir pisze:
Summary:
For the whole software ecosystem:
essentially negligible.
For phase-heavy kernels:
potentially very noticeable.
For DSP/audio/simulation:
a genuinely meaningful idea.
Historically:
it could have been quite powerful.
Mathematically:
it is a very elegant concept.
Architecturally:
the problem is too niche for mainstream x64 ISA support.
sorry for talkin with ai (i uset to talk with myself (its a joke, i was
not talking with myself really just adding thoughts) so now i can talk
withm myself and ai ;c but as this group is not big and in some topic is
not a biger chance for indepth discussion i can post some ai answers
which in turn trigges many f smaller potential points of dicussion if
someone is interested (and if no may skip/ignore..still for me most
important is if subject is good and thoughts are reasonable)
A word of caution. The AI is talking as if you've found something new.
It's actually completely ordinary and well-worn.
But when you need floating-point (and many fields /do/ because of it's properties of varying levels of approximation), you're not just going to
do the work yourself - it's actually pretty hard, so it needs to be in
the language's library for you, and then you may as well get it in
radians because the maths references you use are in radians and who
needs another problem added to their specialism when you're working with approximations anyway?
On 21/05/2026 02:23, Lawrence D?Oliveiro wrote:
On Wed, 20 May 2026 10:03:20 +0200, fir wrote:
Lawrence D?Oliveiro pisze:
i dont know in fact but i dont think so - imo 0...1 has more sense
Radians are the most natural unit for most trig calculations.
In radians,
sin x ? x as x ? 0
But only in radians.
actually sinx -> x as x -> 0
and that's true of any linear function of x defined close to x=0, so
also for degrees and grads.
On 20/05/2026 08:50, Lawrence D?Oliveiro wrote:
On Wed, 20 May 2026 07:29:06 +0200, fir wrote:
i wonder if it would be not good in programing and on cpu level
having a type for angles
it seem ofr sure ot should be form 0.00 to 0.9999999.. so its kinda
float
Radians are the most natural unit for most trig calculations.
<https://gitlab.com/ldo/python_topics_notebooks/-/blob/master/Angle%20Units.ipynb?ref_type=heads>
also quarter turns, i.e. hundredgrads - it "turns" out (ahaha, pun
intended) that the "grad" mode on a scientific calculator is useful
after all.
They're meaningful computationally, especially in a twos-complement unsigned-integer fixed-point representation that overflows gracefully to
0 at 4 (or to -2 at 2 if you choose to see it that way). unsigned and
signed representations are equivalent in this case and there's elegant mathematics related to the indexing of the imaginary unit and base 2 logarithms.
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote or quoted:
ITYM "sin x is approximately = x for small x" which is only gesturally
useful because it doesn't say /how/ approximate for /how/ small - in
A more precise wording might be:
The function f( x )=x is the best affine-linear approximation to
sine at 0 in the sense that it matches the function value and first
derivative at that point (the first-order Taylor polynomial).
, but we also could use wordings that do not refer to derivatives,
The function f( x )=x is the best affine-linear approximation to
sine at 0 in the sense that the error, sin( x )- f( x ), vanishes
strictly faster than linearly as x approaches 0.
, or,
The function f( x )=x is the best linear approximation to sine
at 0 in the sense that it provides the tightest possible linear
upper bound for sine when x > 0 in a neighborhood of 0.
On 12/06/2026 05:50, Stefan Ram wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote or quoted:
ITYM "sin x is approximately = x for small x" which is only gesturally
useful because it doesn't say /how/ approximate for /how/ small - in
A more precise wording might be:
The function f( x )=x is the best affine-linear approximation to
sine at 0 in the sense that it matches the function value and first
derivative at that point (the first-order Taylor polynomial).
, but we also could use wordings that do not refer to derivatives,
The function f( x )=x is the best affine-linear approximation to
sine at 0 in the sense that the error, sin( x )- f( x ), vanishes
strictly faster than linearly as x approaches 0.
, or,
The function f( x )=x is the best linear approximation to sine
at 0 in the sense that it provides the tightest possible linear
upper bound for sine when x > 0 in a neighborhood of 0.
oooh, you give me CHILLS!
Or you could just say, as you did, that sin x ? x as x ? 0. Stefan's
first and third alternatives are not more precise - they just sound
more profound, and are directly derivable from from your wording. His
second alternative is, I think at first glance, untrue.
On 12/06/2026 05:47, Tristan Wibberley wrote:[...]
On 21/05/2026 02:23, Lawrence D?Oliveiro wrote:
On Wed, 20 May 2026 10:03:20 +0200, fir wrote:actually sinx -> x as x -> 0
Lawrence D?Oliveiro pisze:
Radians are the most natural unit for most trig calculations.i dont know in fact but i dont think so - imo 0...1 has more sense
In radians,
sin x ? x as x ? 0
But only in radians.
and that's true of any linear function of x defined close to x=0, so
also for degrees and grads.
No, it is not.
Tristan Wibberley pisze:
On 20/05/2026 08:50, Lawrence D?Oliveiro wrote:
On Wed, 20 May 2026 07:29:06 +0200, fir wrote:
i wonder if it would be not good in programing and on cpu level
having a type for angles
it seem ofr sure ot should be form 0.00 to 0.9999999.. so its kinda
float
Radians are the most natural unit for most trig calculations.
<https://gitlab.com/ldo/python_topics_notebooks/-/blob/master/
Angle%20Units.ipynb?ref_type=heads>
also quarter turns, i.e. hundredgrads - it "turns" out (ahaha, pun
intended) that the "grad" mode on a scientific calculator is useful
after all.
They're meaningful computationally, especially in a twos-complement
unsigned-integer fixed-point representation that overflows gracefully to
0 at 4 (or to -2 at 2 if you choose to see it that way). unsigned and
signed representations are equivalent in this case and there's elegant
mathematics related to the indexing of the imaginary unit and base 2
logarithms.
ye i also thought that thise e^x are not so friendly to computing as 2^x
(but now i m not in mood to go into that to much)
those numbers pi and e come from this sum(z^n/n!)
quite strightforwardly though, and as i said im not so sure if i should
like tehem as they are not quite computational firendly probbaly
(but im not sure how much that yan be avoided mathematically of computationally - and right now im not in a mood to dwell into that)
David Brown <david.brown@hesbynett.no> writes:
On 12/06/2026 05:47, Tristan Wibberley wrote:[...]
On 21/05/2026 02:23, Lawrence D?Oliveiro wrote:
On Wed, 20 May 2026 10:03:20 +0200, fir wrote:actually sinx -> x as x -> 0
Lawrence D?Oliveiro pisze:
Radians are the most natural unit for most trig calculations.i dont know in fact but i dont think so - imo 0...1 has more sense
In radians,
sin x ? x as x ? 0
But only in radians.
and that's true of any linear function of x defined close to x=0, so
also for degrees and grads.
No, it is not.
Yes, it is.
I think the ambiguity of the ? notation might be throwing you off.
What is the limit as x approaches 0 of sin x? The limit is 0 whether
x is expressed in radians, degrees, or anything else.
David Brown <david.brown@hesbynett.no> writes:
[...]
Or you could just say, as you did, that sin x ? x as x ? 0. Stefan's
first and third alternatives are not more precise - they just sound
more profound, and are directly derivable from from your wording. His
second alternative is, I think at first glance, untrue.
But that's true even if x is expressed in radians or degrees, since
sin(x) is continuous and sin(0)=0.
What's more interesting and useful is that sin x / x ? 1 as x ? 0.
On 12/06/2026 13:15, James Kuyper wrote:...
sin x = (e^{ix} - e^(-ix))/2, and the similar formulas for the other
trig functions get more complicated when x is in radians.
I think you meant "when x is /not/ in radians". ...
... But that is not correct. This formula is unchanged, ...
... as are things like
sin(à + ?) = sin(à).cos(?) + cos(à).sin(?)
cos(0) = 1, sin(0) = 0
cos(PI / 2) = 0, sin(PI / 2) = 1
cos(PI) = -1, sin(PI) = 0
...
| Sysop: | Tetrazocine |
|---|---|
| Location: | Melbourne, VIC, Australia |
| Users: | 11 |
| Nodes: | 8 (0 / 8) |
| Uptime: | 220:26:10 |
| Calls: | 219 |
| Files: | 21,505 |
| Messages: | 84,460 |