July 8th, 2018, 04:26 AM  #1 
Member Joined: Sep 2017 From: Saudi Arabia Posts: 37 Thanks: 1  Finding A Point Which Is Equidistant From Given Points Hello my dears, I have 13 distinct points with known coordinates. Is it possible to find a point which is equidistant from the 13 known points? 
July 8th, 2018, 05:18 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,109 Thanks: 1001 
Sorry, but you get NO help until you send Maschke his prize: http://mymathforum.com/lounge/342377competition2.html 
July 8th, 2018, 05:24 AM  #3  
Member Joined: Sep 2017 From: Saudi Arabia Posts: 37 Thanks: 1  Quote:
"The member who collects 10 POINTS, I will send a prize to him via a shipping company."  
July 8th, 2018, 06:12 AM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,070 Thanks: 838 Math Focus: Wibbly wobbly timeywimey stuff.  
July 8th, 2018, 07:43 AM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,109 Thanks: 1001  Quote:
poor Maschke could possibly have spent countless hours getting to 10 points....then to receive a pack of chewing gum as reward  
July 8th, 2018, 11:16 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,614 Thanks: 2603 Math Focus: Mainly analysis and algebra  
July 8th, 2018, 12:38 PM  #7  
Senior Member Joined: Aug 2012 Posts: 2,191 Thanks: 643  Quote:
https://en.wikipedia.org/wiki/Nsphere  
July 8th, 2018, 12:41 PM  #8  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,070 Thanks: 838 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Admittedly the OP wouldn't be considering such. Dan  
July 8th, 2018, 12:47 PM  #9 
Senior Member Joined: Aug 2012 Posts: 2,191 Thanks: 643 
Actually you can do this in the plane if you can pick the metric. You can even do it on a line. The discrete metric is $d(x,y) = 1$ if $x \neq y$ and $d(x,y) = 0$ if $x = y$. Then given any 13 points in the plane or on a line, pick any point distinct from all of them. Then its distance from each of the 13 points is 1. 
October 2nd, 2018, 07:45 AM  #10 
Member Joined: Oct 2018 From: Netherlands Posts: 39 Thanks: 3 
Considering you are a very downtoearth person, I can only imagine you picked 13 geographical points on the surface of the planet and therefore the equidistant point is: "the centre of the earth".
Last edited by Arisktotle; October 2nd, 2018 at 08:25 AM. 

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equidistant, finding, point, points 
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