| Contents |
| We reformulate, in the complex analytic context, the 3-tangent theorem of
Fujiwara-Fukuda-Ozaki; if planar three body orbits has zero linear momentum and
zero angular momentum, then three tangent lines at bodies meet at a point.
Considering the singularities, points at infinity on projective plane, and ramificaiton,
we extend their study of equal mass three-body choreography on the real lemniscate
$(x^2+y^2)^2=x^2-y^2$ to complex projective context, and show that the intersection
points of three tangent lines in the lemniscate case draw a conic, which is the rectangular hyperbola $z^2-w^2=1$ in ${C}^2$ with coordinate system $(z,w)$. And we also describe relate topics. |
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