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Existing of non-intersecting rays

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2

1

$begingroup$

Given $n$ points on a plane, it seems intuitive that it’s possible to draw a ray (half-line) from each point s. t. the $n$ rays do not intersect.

But how to prove this?

geometry

share|cite|improve this question

asked 26 mins ago

athosathos

98611340

$endgroup$

add a comment | 

2

1

$begingroup$

Given $n$ points on a plane, it seems intuitive that it’s possible to draw a ray (half-line) from each point s. t. the $n$ rays do not intersect.

But how to prove this?

geometry

share|cite|improve this question

asked 26 mins ago

athosathos

98611340

$endgroup$

add a comment | 

$begingroup$

Given $n$ points on a plane, it seems intuitive that it’s possible to draw a ray (half-line) from each point s. t. the $n$ rays do not intersect.

But how to prove this?

geometry

share|cite|improve this question

asked 26 mins ago

athosathos

98611340

$endgroup$

share|cite|improve this question

asked 26 mins ago

athosathos

98611340

share|cite|improve this question

asked 26 mins ago

athosathos

98611340

asked 26 mins ago

athosathos

98611340

asked 26 mins ago

athosathos

98611340

1 Answer
1

active

oldest

votes

2

$begingroup$

Pick any point $P$ in the plane that is not on a line containing two or more of the given $n$ points. At each point, draw the ray in the direction away from $P$.

One can in fact do better: It is possible to draw lines through all $n$ points that do not intersect. Choose an orientation that is not parallel to any of the lines between any two of the given points, and draw parallel lines in that orientation through each point.

share|cite|improve this answer

edited 8 mins ago

answered 14 mins ago

FredHFredH

2,6041021

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for being slightly faster than me :)
  $endgroup$
  – Severin Schraven
  14 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thx ! This is a “oh of course “ moment of me
  $endgroup$
  – athos
  13 mins ago
  

  
  
  
  

add a comment | 

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2

$begingroup$

Pick any point $P$ in the plane that is not on a line containing two or more of the given $n$ points. At each point, draw the ray in the direction away from $P$.

One can in fact do better: It is possible to draw lines through all $n$ points that do not intersect. Choose an orientation that is not parallel to any of the lines between any two of the given points, and draw parallel lines in that orientation through each point.

share|cite|improve this answer

edited 8 mins ago

answered 14 mins ago

FredHFredH

2,6041021

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for being slightly faster than me :)
  $endgroup$
  – Severin Schraven
  14 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thx ! This is a “oh of course “ moment of me
  $endgroup$
  – athos
  13 mins ago
  

  
  
  
  

add a comment | 

2

$begingroup$

Pick any point $P$ in the plane that is not on a line containing two or more of the given $n$ points. At each point, draw the ray in the direction away from $P$.

One can in fact do better: It is possible to draw lines through all $n$ points that do not intersect. Choose an orientation that is not parallel to any of the lines between any two of the given points, and draw parallel lines in that orientation through each point.

share|cite|improve this answer

edited 8 mins ago

answered 14 mins ago

FredHFredH

2,6041021

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  +1 for being slightly faster than me :)
  $endgroup$
  – Severin Schraven
  14 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thx ! This is a “oh of course “ moment of me
  $endgroup$
  – athos
  13 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Pick any point $P$ in the plane that is not on a line containing two or more of the given $n$ points. At each point, draw the ray in the direction away from $P$.

One can in fact do better: It is possible to draw lines through all $n$ points that do not intersect. Choose an orientation that is not parallel to any of the lines between any two of the given points, and draw parallel lines in that orientation through each point.

share|cite|improve this answer

edited 8 mins ago

answered 14 mins ago

FredHFredH

2,6041021

$endgroup$

share|cite|improve this answer

edited 8 mins ago

answered 14 mins ago

FredHFredH

2,6041021

answered 14 mins ago

FredHFredH

2,6041021

answered 14 mins ago

FredHFredH

2,6041021