A note on Koide's lepton mass relation

Koide has pointed out that the mass relation $m_e + m_{\mu} + m_{\tau} = {2 \over 3}(\sqrt{m_e} + \sqrt{m_{\mu}} + \sqrt{m_{\tau}})^2$ is consistent with the most recent measurements of the tau lepton mass. We point out that this relation has a geometric interpretation.