Write the distance y across the flat sides of a hexagonal nut as a function of r (see figure in the website below).

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  1. Enclose the hexagon within a square
    Consider the right-angled triangle at the top right.
    It is a 30-60-90° triangle with a hypotenuse of r
    (The sides of this triangle are in the ratio of 1 : √3 : 2 )

    let the side opposite the 60° angle be p
    p/r = √3/2
    p = √3r/2
    but y = 2p = √3r

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