Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Curvature on a curve and circle
Replies: 6   Last Post: Mar 11, 2013 3:54 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Brad Cooper

Posts: 167
Registered: 12/8/04
Curvature on a curve and circle
Posted: Mar 3, 2013 10:16 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

The "well behaved, smooth" function f(x) has endpoints f(0) = f(h) = 0. The
curve of the function has length s1.

An arc of a circle passing through (0, 0) and (0, h) has fixed curvature k
and its arc length is also s1.

It is required to show that a point must exist on f(x) where curvature is
also k.


I have set up a CAS program to simulate the situation and the proposition
held up in every case.

I have been working with the idea that, at the required point, the normal to
f(x) is normal to the circle.

I am not making much headway. Any ideas appreciated.

Cheers,
Brad

--
Number of stars = 10 x Number of grains of sand on all the beaches and
deserts of Earth.





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.