Equilateral triangles of sides \(1, 3, 5, …, 2n−1\), are placed end-to-end along a straight line.

Show that the vertices which do not lie on the line all lie on a parabola and that their focal radii are all integers.

Equilateral triangles of sides \(1, 3, 5, …, 2n−1\), are placed end-to-end along a straight line.

Show that the vertices which do not lie on the line all lie on a parabola and that their focal radii are all integers.

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## Comments

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TopNewestThat's so beautiful! Thanks for sharing :) – Shashwat Shukla · 2 years, 6 months ago

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Hi Megh

Is the equation of the parabola : \( y^{2} = 3(x+\frac{1}{4}) \) ? – Azhaghu Roopesh M · 2 years, 6 months ago

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– U Z · 2 years, 6 months ago

Ok,then?Log in to reply

– Azhaghu Roopesh M · 2 years, 6 months ago

Ok, I'll try posting a proof later on :)Log in to reply