spiral function f[(r)(theta)]

[Oscarville]

Here's the picture I promised of the spiral and its relation to the circle:
http://mathforum.org/kb/servlet/JiveServlet/download/125-2222339-7340047-662693/contuatia%20003.jpg

You can see that s=r(theta), relates to f[(r)(theta)]. Theta should be in radians, I'm assuming. But I wasn't prepared to find the equivalents for degrees, so I expressed everything in degrees.

I hope you can see from the diagram, that as the circle forms, the function, f[(r)(theta)] grows.

It appears to be a spiral of Archimedes, with the center axis, perhaps passing through z=4. It's inverted obviously.

The values are real, so this, once again, is a real function; not simply something I "cooked up."

Anyone can solve this, if they're interested.

Please ask any questions, if you're interested and there's anything you need to know.

Cheers!
-oscar

[gudi]

On Dec 22, 1:46 am, Oscarville <krzysztof-...@hotmail.com> wrote:
> Here's the picture I promised of the spiral and its relation to the circle:

>    http://mathforum.org/kb/servlet/JiveServlet/download/125-2222339-7340...

>
> You can see that s=r(theta), relates to f[(r)(theta)]. Theta should be in radians, I'm assuming. But I wasn't prepared to find the equivalents for degrees, so I expressed everything in degrees.
>
> I hope you can see from the diagram, that as the circle forms, the function, f[(r)(theta)] grows.
>
> It appears to be a spiral of Archimedes, with the center axis, perhaps passing through z=4. It's inverted obviously.
>
> The values are real, so this, once again, is a real function; not simply something I "cooked up."
>
> Anyone can solve this, if they're interested.
>
> Please ask any questions, if you're interested and there's anything you need to know.
>
> Cheers!
> -oscar

It is n't entirely clear. Please look up Cornu's spiral and its
intrinsic diffrl. equation. Do you need to impart torsion to the
spiral or is it in a plane?

Please retain relevant quoted part ( > at start of line ) while
replying.

Narasimham

[Oscarville]

There are quite a few more points included on contuatia 004.jpg. The curve does not impart torsion. It can be represented on a plane.

The principle axises for the spiral are z=4 and y=(7/10)(root 2)(r) - this can be seen in the contuatia 004.jpg)

I admit, I am not ready to unravel the "mysteries" of Cornu's Spiral. Luckily, this curve is not a Cornu Spiral. It is Logarithimic. The center is displaced from the principle axises, by z=4 and y=(7/10)(root 2)r.

Attachment available from http://mathforum.org/kb/servlet/JiveServlet/download/125-2222339-7340932-662805/contuatia%20004.jpg

[Oscarville]

similarities can be seen at this link:

http://mathworld.wolfram.com/LogarithmicSpiral.html

[gudi]

On Dec 23, 10:16 am, Oscarville <krzysztof-...@hotmail.com> wrote:
> There are quite a few more points included on contuatia 004.jpg. The curve does not impart torsion. It can be represented on a plane.

The sketch you made shows x,y and z axes !

Narasimham

>
> The principle axises for the spiral are z=4 and y=(7/10)(root 2)(r) - this can be seen in the contuatia 004.jpg)
>
> I admit, I am not ready to unravel the "mysteries" of Cornu's Spiral. Luckily, this curve is not a Cornu Spiral. It is Logarithimic. The center is displaced from the principle axises, by z=4 and y=(7/10)(root 2)r.
>

> Attachment available fromhttp://mathforum.org/kb/servlet/JiveServlet/download/125-2222339-7340...