On the plane, the sought "equidistant point" makes sense only for those given points which all lay on the same circle. True for two points as well.
For three or more points, you need only any three points and http://www.jsoftware.com/jwiki/Phrases/Geometry#Circlethrough3points > From: Richard Donovan <[email protected]> > > > For "equidistant point" please read "nearest equidistant point" as I just > realised > that with two points only there are an infinite number of "equidistant points" > > > From: [email protected] > > To: [email protected] > > Date: Fri, 30 Oct 2009 09:21:11 +0000 > > Subject: [Jchat] Point equidistant to 3 or more other points > > > > > > Point equidistant to 3 or more other points > > > > Hi! > > > > > > Not specifically related to J, a maths question really, but I will try to > > code > the solution in J! > > > > > > If there are 2 points, (x1 y1) and (x2 y2), the equidistant point is at the > midpoint at location ((x1+x2)/2) ((y1+y2)/2) > > > > > > eg if there are 2 points p and q at locations (1,2) and (3,0) the point > equidistant is at (2,1) - the midpoint m > > > > > > y > > > > 4 | > > > > 3 | > > > > 2 |p > > > > 1 | m > > > > _ |__q_______ x > > > > 0 1 2 3 4 > > > > > > Suppose there are more than 2 points? Is there a formula for working out > > the > point equidistant to the n points? > > > > > > eg if there are 3 points p q r at locations (1,2) (3,0) and (3,2), the > > point equidistant is still at (2,1), but I can't see a way of computing > > this from the figures. > > > > > > y > > > > 4 | > > > > 3 | > > > > 2 |p--r > > > > 1 | m > > > > _ |__q_______ x > > > > 0 1 2 3 4 NB hyphens are spaces-hotmail changes 2 spaces > > to > 1 > > > > > > This is not a test question or homework crib - I am just interested in > mathematics! > > > > > > The thought occured to me and I just cant see a solution for the > > general case finding equidistant point of points (x1 y1) (x2 y2) (x3 y3) ... > > (xn yn) > > > > ...and as for the 3D case (x1 y1 z1) (x2 y2 z2) (x3 y3 z3) ... > > (xn yn zn)......!!!!!! > > > > > > Thanks in advance! > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
