# What is the side length of the smallest sized equilateral triangle that can be placed on the (x,y) plane where all coordinates are integers AND no side is horizontal and no side is vertical?

There is no such triangle, due to

In fact it will lie at the point:

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The side length of the smallest equilateral triangle that can be placed on the (x, y) plane where all coordinates are integers and no side is horizontal and no side is vertical is √3 units.

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