Define Circle Knowing Two Points and ARC LENGTH Only.

  • Thread starter Ryank
  • Start date
  • #1
4
0

Main Question or Discussion Point

I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!
 

Answers and Replies

  • #2
berkeman
Mentor
57,330
7,328
I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!
What is the context of the question? Could you post a sketch? Thanks.
 
  • #3
4
0
There doesn't really need to be a context. You know the length of a chord on the circle and the length of the arc segment between them. I did some digging and did finally manage to find two solutions. One uses Newton's approximation method and the other uses and taylor expansion:

http://norman.rasmussen.co.za/24/radius-from-arc-and-chord-length/
http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 [Broken]
 
Last edited by a moderator:
  • #4
hotvette
Homework Helper
996
5
Looks like case 1 from Dr. Math that requires Newton's Method is the most straightforward.
 
Last edited:
  • #5
5,439
7
Perhaps this sketch will help, it's basic trigonometry.

Since you have fixed two points on the circumference you not only know the arc length you also know the chord length.
 

Attachments

Related Threads on Define Circle Knowing Two Points and ARC LENGTH Only.

Replies
7
Views
6K
Replies
14
Views
6K
Replies
1
Views
1K
Replies
2
Views
772
Replies
3
Views
7K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
770
Replies
4
Views
361
Replies
4
Views
498
Top