--- Wildemar Wildenburger <[EMAIL PROTECTED]>
wrote:
>
>
> Oh my, remember when we used to discuss murderous
> snakes and silly
> British comedians on this group?
> I hardly do ...
> /W
Although all of us are mere amateurs
in this business of making parameters
when it's circles in question
I
--- Peter Otten <[EMAIL PROTECTED]> wrote:
>
> I know not much more about Fourier series than that
> they do exist, so let me
> refer you to
>
> http://en.wikipedia.org/wiki/Fourier_series
>
I'd like to try to bring this thread back full circle
(or maybe at least 7*pi/4).
1) OP posted an ex
Peter Otten wrote:
> [EMAIL PROTECTED] wrote:
>
>
>> sine is a dimensionless value.
>> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
>> etc.
>> you can see that sin can be dimensionless only if x is dimensionless
>> too.
>>
>
> With y = x^2 = 1/3 pi^2 - 4(cos x - cos(2
Wildemar Wildenburger wrote:
> Peter Otten wrote:
>> With y = x^2 = 1/3 pi^2 - 4(cos x - cos(2x)/2^2 + cos(3x)/3^2 - ...)
>>
>> area is dimensionless, too, I suppose.
>>
>
> Ehr, ... maybe this is obvious, but I don't see it: Please explain the
> second equality sign.
I know not much more abo
Peter Otten wrote:
> With y = x^2 = 1/3 pi^2 - 4(cos x - cos(2x)/2^2 + cos(3x)/3^2 - ...)
>
> area is dimensionless, too, I suppose.
>
Ehr, ... maybe this is obvious, but I don't see it: Please explain the
second equality sign.
/W
--
http://mail.python.org/mailman/listinfo/python-list
[EMAIL PROTECTED] wrote:
> sine is a dimensionless value.
> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
> etc.
> you can see that sin can be dimensionless only if x is dimensionless
> too.
With y = x^2 = 1/3 pi^2 - 4(cos x - cos(2x)/2^2 + cos(3x)/3^2 - ...)
area is dimens
Erik Max Francis wrote:
> Wildemar Wildenburger wrote:
>
>
>> So in each term of the sum you have a derivative of f, which in the
>> case of the sine function translates to sine and cosine functions at the
>> point 0. It's not like you're rid of the function just by doing a
>> polynomial exp
Wildemar Wildenburger wrote:
> So in each term of the sum you have a derivative of f, which in the
> case of the sine function translates to sine and cosine functions at the
> point 0. It's not like you're rid of the function just by doing a
> polynomial expansion. The only way to *solve* this
[EMAIL PROTECTED] wrote:
> if you are discordant read more :P :
> sine is a dimensionless value.
> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
> etc.
> you can see that sin can be dimensionless only if x is dimensionless
> too.
>
> I am a professional physicist and a know ab
Gary Herron wrote:
> Wildemar Wildenburger wrote:
>
>> Gary Herron wrote:
>>
>>
>>> Of course not! Angles have units, commonly either degrees or radians.
>>>
>>> However, sines and cosines, being ratios of two lengths, are unit-less.
>>>
>>>
>>>
To understand it: sin
Gary Herron wrote:
>> The radian is defined as the ratio of an arc of circumfence of a circle
>> to the radius of the circle and is therefore *dimensionless*. End of story.
>> http://en.wikipedia.org/wiki/Radian and esp.
>> http://en.wikipedia.org/wiki/Radian#Dimensional_analysis
>>
>>
>>
--- Alex Martelli <[EMAIL PROTECTED]> wrote:
>
> I blame the
> Babylonians for that
> confusion just as much as for the clunky base-60
> that intrudes in our
> ordinary time reckoning...!
>
I apologize for helping to start this whole ridiculous
thread, although I hope some people have been
ente
Gary Herron wrote:
> No, not end-of-story. Neither of us are being precise enough here. To
> quote from your second link:
> "Although the radian is a unit of measure, it is a dimensionless
> quantity."
>
> But NOTE: Radians and degrees *are* units of measure., however those
> units are dime
Gary Herron wrote:
> Of course not! Angles have units, commonly either degrees or radians.
...
> I don't know of any name for the units of "sqrt of angle", but that
> doesn't invalidate the claim that the value *is* a dimensioned
> quantity. In lieu of a name, we'd have to label such a q
[EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
> On 3, 22:07, "[EMAIL PROTECTED]" <[EMAIL PROTECTED]> wrote:
> >
> > angle is a ratio of two length and
> >dimensionless.http://en.wikipedia.org/wiki/Angle#Units_of_measure_for_ang
> >les
> >
> > only dimensionless values can be a argument of a sin
"Steven D'Aprano" <[EMAIL PROTECTED]> writes:
> On Sun, 03 Jun 2007 11:26:40 -0700, [EMAIL PROTECTED] wrote:
>
>> if you are discordant read more :P :
>> sine is a dimensionless value.
>> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
>> etc.
>> you can see that sin can be dim
Wildemar Wildenburger wrote:
> Gary Herron wrote:
>
>> Of course not! Angles have units, commonly either degrees or radians.
>>
>> However, sines and cosines, being ratios of two lengths, are unit-less.
>>
>>
>>> To understand it: sin() can't have dimensioned argument. It is can't
>>> t
Gary Herron wrote:
> Of course not! Angles have units, commonly either degrees or radians.
>
> However, sines and cosines, being ratios of two lengths, are unit-less.
>
>> To understand it: sin() can't have dimensioned argument. It is can't
>> to be - sin(meters)
>>
>>
> No it's sin(rad
On Sun, 03 Jun 2007 11:26:40 -0700, [EMAIL PROTECTED] wrote:
> if you are discordant read more :P :
> sine is a dimensionless value.
> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
> etc.
> you can see that sin can be dimensionless only if x is dimensionless
> too.
>
> I am
What's the square root of -1 radians? :)
Park yourself in front of a world of choices in alternative vehicles. Visit the
Yahoo! Auto Green Center.
http://autos.yahoo.com/green_center/
--
http://mail.p
In article <[EMAIL PROTECTED]>,
Leonhard Vogt <[EMAIL PROTECTED]> wrote:
>>> Yes, I understand that, but what is the geometrical
>>> meaning of the square root of an arc length?
>>
>> That's a different question to your original question, which was asking
>> about the square root of an angle.
>
On 3, 22:07, "[EMAIL PROTECTED]" <[EMAIL PROTECTED]> wrote:
>
> angle is a ratio of two length and
> dimensionless.http://en.wikipedia.org/wiki/Angle#Units_of_measure_for_angles
>
> only dimensionless values can be a argument of a sine and exponent!
> Are you discordant?
if you are discordant
On 3, 21:43, Gary Herron <[EMAIL PROTECTED]> wrote:
> [EMAIL PROTECTED] wrote:
>
> > angle is dimensionless unit.
>
> Of course not! Angles have units, commonly either degrees or radians.
>
> However, sines and cosines, being ratios of two lengths, are unit-less.> To
> understand it: sin() ca
[EMAIL PROTECTED] wrote:
> On 3, 14:05, Steven D'Aprano <[EMAIL PROTECTED]>
> wrote:
>
>> On Sun, 03 Jun 2007 09:02:11 +0200, Leonhard Vogt wrote:
>>
bla-bla
>> Hmmm... perhaps that's why the author of the "units" program doesn't
>> treat angles as dimensionless when
On 3, 14:05, Steven D'Aprano <[EMAIL PROTECTED]>
wrote:
> On Sun, 03 Jun 2007 09:02:11 +0200, Leonhard Vogt wrote:
> >> bla-bla
>
> Hmmm... perhaps that's why the author of the "units" program doesn't
> treat angles as dimensionless when taking square roots.
>
> Given that, I withdraw my claim
On Sun, 03 Jun 2007 09:02:11 +0200, Leonhard Vogt wrote:
>> Angles are a ratio of two lengths, and are therefore dimensionless units.
>> So the square root of an angle is just another angle, in the same units,
>> and it requires no special geometric interpretation: the square root of 25
>> degree
>> Yes, I understand that, but what is the geometrical
>> meaning of the square root of an arc length?
>
> That's a different question to your original question, which was asking
> about the square root of an angle.
>
>> And what would the units be?
>
> Angles are a ratio of two lengths, and
"Steve Howell" wrote:
>
> --- Steven D'Aprano
> <[EMAIL PROTECTED]> wrote:
> > Angles are real numbers (in the maths sense), so
> > sqrt(pi/4) radians is
> > just as reasonable an angle as pi/4 radians. Both
> > are irrational numbers
> > (that is, can't be written exactly as the ratio of
>
On Sat, 02 Jun 2007 08:29:59 -0700, Steve Howell wrote:
>
> --- Steven D'Aprano
> <[EMAIL PROTECTED]> wrote:
>
>> On Sat, 02 Jun 2007 05:54:51 -0700, Steve Howell
>> wrote:
>>
>> >>
>> >>def f(x): y = x*x; return sin(y)+cos(y);
>> >>
>> >
>> > Although I know valid trigonometry is not th
--- Steven D'Aprano
<[EMAIL PROTECTED]> wrote:
> On Sat, 02 Jun 2007 05:54:51 -0700, Steve Howell
> wrote:
>
> >>
> >>def f(x): y = x*x; return sin(y)+cos(y);
> >>
> >
> > Although I know valid trigonometry is not the
> point of
> > this exercise, I'm still trying to figure out why
> > an
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