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Math Help - Minimum Surface Area of a Honeycomb

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    Minimum Surface Area of a Honeycomb

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    S'(\theta) = \frac{3s^2}{2}\left[\frac{\sin^2{\theta} - (\sqrt{3}-\cos{\theta})\cos{\theta}}{\sin^2{\theta}}\right]

    S'(\theta) = 0 if

    \sin^2{\theta} - (\sqrt{3}-\cos{\theta})\cos{\theta} = 0

    \sin^2{\theta} - \sqrt{3}\cos{\theta} + \cos^2{\theta} = 0

    1 - \sqrt{3}\cos{\theta} = 0

    \theta = \arccos\left(\frac{1}{\sqrt{3}}\right)
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