How can one calculate the probability that any line is on lattice point?

Multi tool use
Multi tool use

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite
1












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.










share|cite|improve this question























  • What are your own thoughts about the problem? On what grounds do you choose this line?
    – Matti P.
    Sep 6 at 10:34










  • probability is 0
    – 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.
    – Lingard
    Sep 6 at 10:47










  • to Kenta . why?
    – 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?
    – David K
    Sep 7 at 0:58














up vote
0
down vote

favorite
1












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.










share|cite|improve this question























  • What are your own thoughts about the problem? On what grounds do you choose this line?
    – Matti P.
    Sep 6 at 10:34










  • probability is 0
    – 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.
    – Lingard
    Sep 6 at 10:47










  • to Kenta . why?
    – 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?
    – David K
    Sep 7 at 0:58












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





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.










share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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?
    – Matti P.
    Sep 6 at 10:34










  • probability is 0
    – 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.
    – Lingard
    Sep 6 at 10:47










  • to Kenta . why?
    – 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?
    – David K
    Sep 7 at 0:58
















  • What are your own thoughts about the problem? On what grounds do you choose this line?
    – Matti P.
    Sep 6 at 10:34










  • probability is 0
    – 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.
    – Lingard
    Sep 6 at 10:47










  • to Kenta . why?
    – 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?
    – David K
    Sep 7 at 0:58















What are your own thoughts about the problem? On what grounds do you choose this line?
– Matti P.
Sep 6 at 10:34




What are your own thoughts about the problem? On what grounds do you choose this line?
– Matti P.
Sep 6 at 10:34












probability is 0
– Kenta S
Sep 6 at 10:42




probability is 0
– 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.
– 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.
– Lingard
Sep 6 at 10:47












to Kenta . why?
– Lingard
Sep 6 at 10:48




to Kenta . why?
– 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?
– 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?
– David K
Sep 7 at 0:58















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2907311%2fhow-can-one-calculate-the-probability-that-any-line-is-on-lattice-point%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2907311%2fhow-can-one-calculate-the-probability-that-any-line-is-on-lattice-point%23new-answer', 'question_page');

);

Post as a guest













































































U8htniuqGjgm,aWCT1qWezGIaSqgs,W 3,79RfwE DfNtNf1,Rx
GNMB,sdb P9,1y2cJq0SHph87dIcw4Oi,DJUz YFKzuWUNWcd8wElo25JU,7lnhe,Gnwa,DpMLlXJ tzb879

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

Propositional logic and tautologies

Distribution of Stopped Wiener Process with Stochastic Volatility