Calculating a Circle Through 3 Points - Equations and Confusion

[zmonk85]

Homework Statement

I was looking at the following tutorial

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

Homework Equations

equations 31-34 o the link

The Attempt at a Solution

My question is just whether this means that for 31-34, the answers are determinants of 3x3 matricies?

Also, the nonliniarity for x^2 + y^2 is confusing. Do I treat it the same or do we have to get rid of the 2nd power by taking a derivative like in least squares?

Any help greatly appreciated.

 

[Dick]

Homework Statement

I was looking at the following tutorial

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

Homework Equations

equations 31-34 o the link

The Attempt at a Solution

My question is just whether this means that for 31-34, the answers are determinants of 3x3 matricies?

Also, the nonliniarity for x^2 + y^2 is confusing. Do I treat it the same or do we have to get rid of the 2nd power by taking a derivative like in least squares?

Any help greatly appreciated.

I don't think the Mathworld pages are really intended to be tutorials. They are just places to look up a bunch of stuff of wildly varying levels. If you are given three points A, B and C and want to find the equation of the the circle passing through them using those determinants is likely not the easiest way to go about it. Try intersecting the line equations for the perpendicular bisectors of AB and BC to find the center.

 

[SteamKing]

Eqs. 31-34 are merely formulas expressing how to calculate the quantities a, d, e, and f, which in turn are used to calculate the radius r of the circle (Eq. 30) and the coordinates of the center of the circle (Eqns. 28 and 29). The values inside the determinant expressions are calculated from the coordinates of the three points through which the circle must pass. I don't understand why you are talking about derivatives, since this is a straight-up numerical calculation. These formulas are intended for use in a field like computer graphics, where a geometric procedure is not suitable for use.