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I'm not a mathematician. Can I prove this by just providing an example? My points are (0,0), (0,sqrt(2)), (sqrt(8),0). This should give irrational side lengths
by Invictus0 6y ago
I'm not a mathematician.
Can I prove this by just providing an example? My points are (0,0), (0,sqrt(2)), (sqrt(8),0). This should give irrational side lengths of sqrt(2), sqrt(8), and sqrt(10). The area of this triangle is 2, which is rational.
I solved this by guessing and checking the square roots of positive integers.
- im3w1l 6y agoThe question asks you to prove that it works for every n>=3. So you have to show it works also for n=4, n=5 etc. You are on the right track with square roots though.
- hugodutka 6y agoYou have proved it for n = 3, but you haven't for n >= 4, which the problem also requires.
- kosievdmerwe 6y agoYeah, an alternate phrasing could be "For all integers n >= 3, show that there exists a set of n points in the plane such that the distance between any two points is irrational and each set of three points determines a non-degenerate triangle with rational area." For only having to find a specific n the phrasing would be something like "Find an integer n >= 3, such that ..." But in general a good heuristic is that if your solution is really simple odds are you've misunderstood the problem. IMO problems aren't easy. Even the "easy" ones take a bit of work.