Math Is Fun Forum

Reuel

Member

Registered: 2010-11-28

Posts: 178

Line segments within circles - terminology and proper algebra

Hello. I have a question about the proper terminology and algebraic communication involved in line segments within circles. I am okay at mathematics but I have never had any training on WRITING math.

Questions on algebraic language

1. Imagine you have a circle and there is a line segment within the circle but the line segment does not touch the circle itself and it is not related to anything outside of the circle. What is the proper algebraic expression for the segment and how it relates to the circle? You know, a set of points that are in the circle, etc. In addition, how would you state this scenerio mathematically for the specific case where the segment passes through the circle's center?

2. How would you write (1) for multiple segments, especially for ones that all cross through the circle's center?

3. Would it be better to state the segments as segments e.g. PQ or as vectors?

Questions on terminology

1. Is "uniform curve" a proper term for a circle? Can it be used to describe a circle?

2. Can a line segment within a circle be called a convex hull?

3. If two line segments within a circle both pass through the circle's center (so they share a point) can the circle's center be called a convex combination of the two line segments and/or their end points?

Thanks to all who answer.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Line segments within circles - terminology and proper algebra

hi Reuel,

I've never met a word used for lines inside a circle, not touching the circumference.  I had a quick search on-line and couldn't come up with anything I'm afraid.

If you want to determine whether a line has this property I think you would need to test the end-points, to see if they lie inside the circumference.

eg.

where (a,b) is the centre, and r the radius.

For the line to go through the centre you need to test if (a,b) is on the line.  If the endpoints are (x1,y1) and (x2,y2), you could test the gradient:

If you do a search for 'uniform curve' you'll find lots of curves that are not circles.  So I wouldn't describe a circle this way.

Convex hull ?  Have a look at

http://en.wikipedia.org/wiki/Convex_hull

Similarly for convex combination

http://en.wikipedia.org/wiki/Convex_combination

Bob

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Children are not defined by school ...........The Fonz
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ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Line segments within circles - terminology and proper algebra

Uniform curve as a circle? Most likely not.