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Length of a sine curve

blckwtr
1-Newbie
1-Newbie
‎Mar 20, 2009 03:00 AM
‎Mar 20, 2009 03:00 AM

Length of a sine curve

How do I calculate the length of a sine curve?
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8 REPLIES 8
Fred_Kohlhepp
23-Emerald I
23-Emerald I
(To:blckwtr)
‎Mar 20, 2009 03:00 AM
‎Mar 20, 2009 03:00 AM

From the quicksheets:

Fred Kohlhepp
fkohlhepp@sikorsky.com
path integral.mcd
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Luc_Meekes-disa
1-Newbie
1-Newbie
(To:Fred_Kohlhepp)
‎Mar 20, 2009 03:00 AM
‎Mar 20, 2009 03:00 AM

Yes, this can be done numerically.
I remember discussing the matter with a math teacher at the university, where we tried to solve it symbolically: the symbolic solution does not exis. (Or it has been found sometime over the past 30 years).

Success!

Luc
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ptc-1368288
1-Newbie
1-Newbie
(To:Luc_Meekes-disa)
‎Mar 20, 2009 03:00 AM
‎Mar 20, 2009 03:00 AM

On 3/20/2009 5:39:21 PM, Luc_Meekes wrote:
>Yes, this can be done
>numerically.
>I remember discussing the
>matter with a math teacher at
>the university, where we tried
>to solve it symbolically: the
>symbolic solution does not
>exis. (Or it has been found
>sometime over the past 30
>years).
>
>Success!
>
>Luc
________________________

I don't understand Luc,

The arc length of a curve has an analytical definition for centuries. Do you mean that for sin(x) it fails analytically speaking for some mathematical reason ? Nice to know if you can confirm it is a conjecture, that I then missed to recollect.

jmG
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StuartBruff
23-Emerald II
23-Emerald II
(To:ptc-1368288)
‎Mar 21, 2009 03:00 AM
‎Mar 21, 2009 03:00 AM

collab - calculus arc length 01.mcd
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Luc_Meekes-disa
1-Newbie
1-Newbie
(To:ptc-1368288)
‎Mar 22, 2009 03:00 AM
‎Mar 22, 2009 03:00 AM

Jean,

Stuart's exercise shows what I'm talking about; the problem we were facing back then:
While it is fairly easy to describe it in terms of an integral, the (primitive, "simple") function that describes the arc length of a sine curve is unknown.

Luc
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StuartBruff
23-Emerald II
23-Emerald II
(To:Luc_Meekes-disa)
‎Mar 22, 2009 03:00 AM
‎Mar 22, 2009 03:00 AM

On 3/22/2009 5:58:21 PM, Luc_Meekes wrote:
== Stuart's exercise shows what I'm talking about; the problem we were facing back then:
While it is fairly easy to describe it in terms of an integral, the (primitive, "simple") function that describes the arc length of a sine curve is unknown.

Interestingly, M14 doesn't give the expanded answer that M11 does. M11 expresses the result in terms of the Complete Elliptic Integral of the Second Kind. This is turn can be defined in terms of the Gauss Hypergeometric Function (fhyper in Mathcad).

Stuart
collab - calculus arc length 02.mcd
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ptc-1368288
1-Newbie
1-Newbie
(To:Luc_Meekes-disa)
‎Mar 22, 2009 03:00 AM
‎Mar 22, 2009 03:00 AM

On 3/22/2009 5:58:21 PM, Luc_Meekes wrote:
>Jean,
>
>Stuart's exercise shows what
>I'm talking about; the problem
>we were facing back then:
>While it is fairly easy to
>describe it in terms of an
>integral, the (primitive,
>"simple") function that
>describes the arc length of a
>sine curve is unknown.
>
>Luc
______________________________

Thanks Luc,

I will visit, and read again the long forgotten "Osculating circle".

Jean



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