On the number of lines of given points - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T06:47:22Z http://mathoverflow.net/feeds/question/93796 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/93796/on-the-number-of-lines-of-given-points On the number of lines of given points rose 2012-04-11T19:17:53Z 2012-04-15T16:32:33Z <p>Hi all, I have a question Concerning Beck's theorem. I have read it from <a href="http://en.wikipedia.org/wiki/Beck%27s_theorem" rel="nofollow">http://en.wikipedia.org/wiki/Beck%27s_theorem</a> and I have two questions :</p> <ol> <li><p>I suppose Beck's theorem doesn't hold when instead of saying "at least two points" we take "exactly two points",since there may be lines which do not connect exactly two points at all, right?</p></li> <li><p>In the proof mentioned above, I think the statement that <strong><em>"The lines that connect these pairs either pass through fewer than 2C points, or pass through more than n/C points."</em></strong> is incorrect, it should be "fewer than C points" or more than "2n/C points". Am I right or do I miss some logic here?</p></li> </ol> <p>thanks</p> http://mathoverflow.net/questions/93796/on-the-number-of-lines-of-given-points/94129#94129 Answer by domotorp for On the number of lines of given points domotorp 2012-04-15T16:32:33Z 2012-04-15T16:32:33Z <p>1, Yes, it only holds with at least two, otherwise you get the ordinary lines problem, for which the answer is linear in n, for more see <a href="http://mathworld.wolfram.com/OrdinaryLine.html" rel="nofollow">http://mathworld.wolfram.com/OrdinaryLine.html</a></p> <p>2, No, you miss something, I think it is correct on wikipedia (or I miss some logic...)</p>