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Existing of non-intersecting rays
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Existing of non-intersecting rays
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$begingroup$
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
asked 24 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
asked 24 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
asked 24 mins ago
athosathos
98611340
$endgroup$
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
geometry
asked 24 mins ago
athosathos
98611340
asked 24 mins ago
athosathos
98611340
asked 24 mins ago
athosathos
98611340
asked 24 mins ago
athosathos
98611340
asked 24 mins ago
athosathos
98611340
98611340
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered 13 mins ago
FredHFredH
2,6041021
$endgroup$
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 mins ago
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
answered 13 mins ago
FredHFredH
2,6041021
$endgroup$
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 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.
answered 13 mins ago
FredHFredH
2,6041021
$endgroup$
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 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.
answered 13 mins ago
FredHFredH
2,6041021
$endgroup$
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.
answered 13 mins ago
FredHFredH
2,6041021
edited 7 mins ago
answered 13 mins ago
FredHFredH
2,6041021
answered 13 mins ago
FredHFredH
2,6041021
answered 13 mins ago
FredHFredH
2,6041021
2,6041021
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 mins ago
add a comment |
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 mins ago
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
+1 for being slightly faster than me :)
$endgroup$
– Severin Schraven
12 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 mins ago
$begingroup$
Thx ! This is a “oh of course “ moment of me
$endgroup$
– athos
11 mins ago
add a comment |
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