Point equidistant to 3 or more other points

[Richard Donovan]

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!

                       

                       
               
             
_________________________________________________________________
New Windows 7: Simplify what you do everyday. Find the right PC for you.
http://www.microsoft.com/uk/windows/buy/
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[Richard Donovan]

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: rsdonovan@...
> To: chat@...
> 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!
>
>
>
>
>
>    
> _________________________________________________________________
> New Windows 7: Simplify what you do everyday. Find the right PC for you.
> http://www.microsoft.com/uk/windows/buy/
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm

     
_________________________________________________________________
New Windows 7: Simplify what you do everyday. Find the right PC for you.
http://www.microsoft.com/uk/windows/buy/
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[John Randall-3]

Richard Donovan wrote:

> Suppose there are more than 2 points? Is there a formula for working out
> the point equidistant to the n points?

The points equidistant from P and Q lie on the perpendicular bisector
of the line segment PQ.

The points equidistant from P, Q and R lie on the intersection of the
perpendicular bisectors of PQ, QR and PR.  This intersection may not
exist (e.g. P=(0,0), Q=(0,1), R=(0,2)).  Alternatively, a point
equidistant from P, Q, R is the center of the circle through P, Q, R
(if it exists).  This is easily generalizable to n points.

Best wishes,

John


----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[James C Field]

I suggest you explore the internet and refer to printed versions of
basic geometry. The answer to your problem can be solved with PAPER and
PENCIL.

J is a language concerned with problems MUCH more complex than yours.

First... Draw a pencil diagram of the problem.
Second ... Draw a sketch reconsidering the initial parameters of the
problem.
Third...stop and think and the go to bed .... think again in the
morning. IT IS AMAZING HOW SMART YOU CAN BE IN THE MORNING!

Richard Donovan wrote:

> 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!
>
>
>
>
>
>    
> _________________________________________________________________
> New Windows 7: Simplify what you do everyday. Find the right PC for you.
> http://www.microsoft.com/uk/windows/buy/
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
>  

----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[Oleg Kobchenko]

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 <rsdonovan@...>
>
>
> 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: rsdonovan@...
> > To: chat@...
> > 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

[Oleg Kobchenko]

> J is a language concerned with problems MUCH more complex than yours.


This is a misconception.

> From: James C Field <jamescfield@...>
>
> I suggest you explore the internet and refer to printed versions of
> basic geometry. The answer to your problem can be solved with PAPER and
> PENCIL.
>
> J is a language concerned with problems MUCH more complex than yours.
>
> First... Draw a pencil diagram of the problem.
> Second ... Draw a sketch reconsidering the initial parameters of the
> problem.
> Third...stop and think and the go to bed .... think again in the
> morning. IT IS AMAZING HOW SMART YOU CAN BE IN THE MORNING!
>
> Richard Donovan wrote:
> > 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!
> >
> >            
> >
> >            
> >        
> >                                
> > _________________________________________________________________
> > New Windows 7: Simplify what you do everyday. Find the right PC for you.
> > http://www.microsoft.com/uk/windows/buy/
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> >
> >  
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm

     
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[Devon McCormick]

For the mid-point of any two points - which is the nearest equidistant
point:
   pts=. 1 2,:3 0
   mean pts
2 1
   dis=. 4 : '%:+/*:x-y'"1
   pts dis mean pts
1.4142136 1.4142136

For three points in a plane there is no solution if they are co-linear but
if they are a triangle, the intersection of perpendicular bisectors is the
equidistant point - see
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2003.Su/Messig/assignment4/trianglearecyclic.html.

See "xyrf3P" at
http://www.jsoftware.com/jwiki/Phrases/Geometry#Circlethrough3points for a
function for this, e.g.

   ]rndtri=. ?3 2$10        NB. Random triangle
5 5
5 3
8 0
   edp=. 2{.xyrf3P rndtri   NB. Equidistant point
NB. Graph the three points in green, the equidistant point in blue and draw
red lines to show
NB. the distances.
   pd 'reset'
   pd 'type line;pensize 2;color RED'
   pd ,&.>(<"1 |:rndtri),.&.>edp
   pd 'type point;pensize 5;color BLUE'
   pd <"1 edp,.edp
   pd 'type point;pensize 4;color GREEN'
   pd <"1 |:rndtri
   pd 'show'

For more than three points, I think there's only a solution if the points
are on a circle.

On Fri, Oct 30, 2009 at 5:21 AM, Richard Donovan <rsdonovan@...>wrote:

>
> 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!
>
>
>
>
>
>
> _________________________________________________________________
> New Windows 7: Simplify what you do everyday. Find the right PC for you.
> http://www.microsoft.com/uk/windows/buy/
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>

--
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

[Alex Rufon]

I agree.

Take for example computing for all materials needed to manufacture a bulk order of t-shirts (also in manufacturing as Raw Material Requirement). Its basic arithmetic. Just find out how many materials are needed to make one t-shirt and multiply it by the number of orders by the buyer plus allowance ... and I use J for this.

The problem described was more complex than mine. :P

-----Original Message-----
From: chat-bounces@... [mailto:chat-bounces@...] On Behalf Of Oleg Kobchenko
Sent: Saturday, October 31, 2009 8:41 AM
To: Chat forum
Subject: Re: [Jchat] Re High school algebra

> J is a language concerned with problems MUCH more complex than yours.


This is a misconception.

> From: James C Field <jamescfield@...>
>
> I suggest you explore the internet and refer to printed versions of
> basic geometry. The answer to your problem can be solved with PAPER and
> PENCIL.
>
> J is a language concerned with problems MUCH more complex than yours.
>
> First... Draw a pencil diagram of the problem.
> Second ... Draw a sketch reconsidering the initial parameters of the
> problem.
> Third...stop and think and the go to bed .... think again in the
> morning. IT IS AMAZING HOW SMART YOU CAN BE IN THE MORNING!
>
> Richard Donovan wrote:
> > 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!
> >
> >            
> >
> >            
> >        
> >                                
> > _________________________________________________________________
> > New Windows 7: Simplify what you do everyday. Find the right PC for you.
> > http://www.microsoft.com/uk/windows/buy/
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> >
> >  
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm

     
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm