Poncelet's Closure Theorem
If an -sided Poncelet
Transverse constructed for two given Conic
Sections is closed for one point of origin, it is closed for any position
of the point of origin. Specifically, given one Ellipse
inside another, if there exists one Circuminscribed
(simultaneously inscribed in the outer and circumscribed on the inner) -gon,
then any point on the boundary of the outer Ellipse
is the Vertex
of some Circuminscribed-gon.
References
Dörrie, H. 100
Great Problems of Elementary Mathematics: Their History and Solutions.
New York: Dover, p. 193, 1965.
© 1996-9 Eric W. Weisstein
1999-05-26