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#ApproximateInteger

Richard PennerArpie4Math@mathstodon.xyz
2023-01-13

@jamestanton@twitter.com (gdaymath.com/) writes (twitter.com/jamestanton/status):
“It is impossible to draw an equilateral triangle on a square lattice of dots with each vertex on a dot. (Why?) But can we get close?

Is it possible to have two vertices on a dot and the third within 0.00000001 units from a dot?

(The picture is not equilateral.)”

#geometry #math #ContinuedFractions #ApproximateInteger #PicksTheorem

A pink, near-equilateral triangle is drawn on a square lattice of green points with vertices at lattice points. The sides are √25, √26, and √29 in units of the lattice spacing, or approximately 5, 5.1, and 5.4 units, respectively. This relates to the claim that 3 distinct lattice points cannot form an equilateral triangle.

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