= Tusi couple
{c}
{title2=$R(e^{i\theta}+e^{-i\theta})=2R\cos\theta$}
{wiki}
Two uniform <circular motions> of radius $R$ and opposite angular rates sum to rectilinear oscillation: $R(\cos\theta,\sin\theta)+R(\cos\theta,-\sin\theta)=(2R\cos\theta,0)$. Geometrically, a circle of radius $R$ rolls inside one of radius $2R$; a marked point traces a diameter. This plane construction must be distinguished from spherical variants, which need their own geometric argument.<The Spherical Case of the Tūsī Couple by George Saliba and E. S. Kennedy>[research abstract: distinction between plane and spherical versions]{ref}
\Image[/tusi-couple.png]
{title=Three positions of the Tusi couple: the sum of two equal circular radius vectors stays on a diameter}
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