- #1
courtrigrad
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Hello all
In a ordinary syatem of rectangular coordinates, the points for which both coordinates are integers are called lattice points . Prove that a triangle whose vertices are lattice points cannot be equilateral. Ok so I know that in a equilateral triangle the angle measures are [tex] \frac{\pi}{3} [/tex].Assuming that we do have an equilateral triangle then we know that [tex] \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} [/tex] which is irrational. Hence we cannot have lattice points.
Is this sufficient enough to qualify as a proof?
Thanks
In a ordinary syatem of rectangular coordinates, the points for which both coordinates are integers are called lattice points . Prove that a triangle whose vertices are lattice points cannot be equilateral. Ok so I know that in a equilateral triangle the angle measures are [tex] \frac{\pi}{3} [/tex].Assuming that we do have an equilateral triangle then we know that [tex] \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} [/tex] which is irrational. Hence we cannot have lattice points.
Is this sufficient enough to qualify as a proof?
Thanks
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