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Name: Jeff P.
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
I would like to create some displays for our school's web site that use items distributed in circles to illustrate ideas. I thought I'd put together a function in Flash that would do the distribution for me. I'm getting lost in mathematical research which, though interesting, is taking too much time. I need a mathematician! In particular, I need equations for determining a point on a circle given the number of equidistant points, which point in the sequence I'm looking for, and the radius. So: circlePoint (instances, item, radius) would return x,y coordinates for the point in position "item" of "instances" on the circle whose radius is "radius" from (0,0). Any assumed position [(0,r), (r,0), etc.] for the first point in the sequence is OK. I don't need program code, just the mathematics. Our teachers and students (and I!) thank you for any and all assistance.



Replies:
I am not sure I follow exactly where your question is leading. Nonetheless, the following two equations tell just about anything you need to know about circles:

1. An especially compact and elegant equation of a circle is:
((x-h)/R)^2 + ((y-k)/R)^2 = 1 where, (x,y) are the coordinates of points on the circle, R is the radius, and (h,k) is the location of the origin of the circle. This is called the center/radius form.

2. The most general equation for a circle is:
x^2 +y^2 +D*x +E*y +F = 0 Given the coordinates of any three points: (x1,y1) ; (x2,y2) ; (x3,y3) gives a system of linear equations in three unknowns: D, E, and F in terms of the coordinates of the three points. Solving that system of equations gives the equation of the circle containing the three points.

Good Luck,

Vince Calder


Jeff,

Trigonometry is your tool for this problem. You will be dividing the 360 degree circle into "instances" parts. Let "angle" be (360)/"instances". You want to 'rotate' a multiple of this "angle" for each item. Let your x coordinate be "radius" * Cosine("item" * "angle"). Let your y-coordinate be "radius" * Sine("item" * "angle"). To adjust positions, you can add or subtract any angle from your function argument. It is just VERY IMPORTANT that both functions have exactly the same argument.

Note: Some programs and languages use the full words sine and cosine. Some use SIN and COS.

Dr. Ken Mellendorf



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