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You are not logged in. #1 20110731 04:40:59
points with integer distancesHow many points can be placed in the plane so that the distance between every pair of points is an integer? What about in higher dimensions? #2 20110731 14:26:53
Re: points with integer distancesHi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #3 20110731 18:30:48
Re: points with integer distanceshi
Do you mean the same, constant, integer? OR may we consider eg. 3, 4, 5 as an acceptable answer? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #4 20110801 16:46:44
Re: points with integer distancesI meant the points to be noncolinear, distances can be any integer. In 2D the best I can find is 4 points in a 3X4 rectangle or any other rectangle based on a pythagorean triple. #5 20110801 16:59:10
Re: points with integer distancesOk. Last edited by bob bundy (20110801 22:32:00) You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20110803 09:46:04
Re: points with integer distancesIn the xyplane, look at Signature line: I wish a had a more interesting signature line. #7 20110803 13:27:00
Re: points with integer distancesHe wants the points to be noncollinear. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #8 20110803 18:18:30
Re: points with integer distancesHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20110803 18:29:01
Re: points with integer distanceshi bobbym You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20110803 18:41:30
Re: points with integer distancesHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20110803 19:24:50
Re: points with integer distancesHi bobbym, Last edited by gAr (20110803 19:26:40) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #12 20110803 19:26:37
Re: points with integer distanceshi bobbym and gAr Last edited by bob bundy (20110803 19:37:46) You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #13 20110803 19:43:15
Re: points with integer distancesHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20110803 19:43:41
Re: points with integer distancesHi Bob, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #15 20110803 19:56:32
Re: points with integer distancesHi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #16 20110803 20:27:04
Re: points with integer distancesHi gAr; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20110803 20:38:15
Re: points with integer distancesHi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #18 20110803 20:43:23
Re: points with integer distancesHi gAr; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20110803 21:09:04
Re: points with integer distancesHi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #20 20110803 21:18:33
Re: points with integer distances
That is true. It is one type of solution. The other type has a bunch of points with one set of three collinear. That is a known solution. For anything else no one knows. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20110803 21:24:27
Re: points with integer distancesOkay. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #22 20110803 21:29:53
Re: points with integer distancesHi gAr; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #23 20110803 21:39:18
Re: points with integer distancesOkay. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #24 20110803 22:41:30
Re: points with integer distancesI think we have shown that we can generate as many points as needed. That answers the question for 2D. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #25 20110803 22:53:36
Re: points with integer distancesYes, and for 3D, the eqivalent would be a sphere. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." 