How can one calculate the probability that any line is on lattice point?
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In plane coordinates, how can one calculate the probability that any line is on lattice point?
If you add set theory grounds about solving this problem, I would be very thankful.
I am a korean highschooler. I'm sorry that my English is so poor.
probability
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up vote
0
down vote
favorite
In plane coordinates, how can one calculate the probability that any line is on lattice point?
If you add set theory grounds about solving this problem, I would be very thankful.
I am a korean highschooler. I'm sorry that my English is so poor.
probability
What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
probability is 0
â Kenta S
Sep 6 at 10:42
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
to Kenta . why?
â Lingard
Sep 6 at 10:48
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In plane coordinates, how can one calculate the probability that any line is on lattice point?
If you add set theory grounds about solving this problem, I would be very thankful.
I am a korean highschooler. I'm sorry that my English is so poor.
probability
In plane coordinates, how can one calculate the probability that any line is on lattice point?
If you add set theory grounds about solving this problem, I would be very thankful.
I am a korean highschooler. I'm sorry that my English is so poor.
probability
probability
edited Sep 6 at 12:41
Bernard
112k635104
112k635104
asked Sep 6 at 10:27
Lingard
1
1
What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
probability is 0
â Kenta S
Sep 6 at 10:42
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
to Kenta . why?
â Lingard
Sep 6 at 10:48
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58
add a comment |Â
What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
probability is 0
â Kenta S
Sep 6 at 10:42
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
to Kenta . why?
â Lingard
Sep 6 at 10:48
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58
What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
probability is 0
â Kenta S
Sep 6 at 10:42
probability is 0
â Kenta S
Sep 6 at 10:42
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
to Kenta . why?
â Lingard
Sep 6 at 10:48
to Kenta . why?
â Lingard
Sep 6 at 10:48
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58
add a comment |Â
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What are your own thoughts about the problem? On what grounds do you choose this line?
â Matti P.
Sep 6 at 10:34
probability is 0
â Kenta S
Sep 6 at 10:42
choosing depends on only random. I think that it would be 0. because in case that slope and y-intercept are e(exponential), it isn't on lattice point. cause irrational number set is larger than rational number set, I think that because of many irrational number, it would be 0.
â Lingard
Sep 6 at 10:47
to Kenta . why?
â Lingard
Sep 6 at 10:48
Probability requires a probability distribution. There is no uniform probability distribution over the entire plane, so we have to choose something else. A random point in the square $[0,1]times[0,1],$ and a line at a random angle through that point, might be suitable. Are you familiar with Buffon's needle problem?
â David K
Sep 7 at 0:58