References
- Daepp, U., Gorkin, P., Mortini, R. (2002). Ellipses and finite Blaschke products. Amer. Math. Monthly. 109(9): 785–795. DOI: 10.1080/00029890.2002.11919914.
- Daepp, U., Gorkin, P., Shaffer, A., Voss, K. (2018). Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other. Carus Mathematical Monographs, Vol. 34. Providence, RI: MAA Press.
- Gardner, M. (1995). New Mathematical Diversions. Revised edition. MAA Spectrum. Washington, DC: Mathematical Association of America.
- Halbeisen, L., Hungerbühler, N. (2015). A simple proof of Poncelet’s theorem (on the occasion of its bicentennial). Amer. Math. Monthly. 122(6): 537–551. doi.org/ DOI: 10.4169/amer.math.monthly.122.6.537.
- Poncelet, J. V. (1865–1866). Traité des propriétés projectives des figures: ouvrage utile à qui s’occupent des applications de la géométrie descriptive et d’opérations géométriques sur le terrain, Vols. 1–2, 2nd ed. Paris: Gauthier-Villars.
- Simonič, A. (2018). Calculus style proof of Poncelet’s theorem for two ellipses. Elem. Math. 73(4): 145–150. DOI: 10.4171/EM/367.
- Summary
- In an article entitled The Ellipse, Martin Gardner explains a simple way to “fold” an ellipse inside a circle. It is surprising that an ellipse appears through folding, but there are more surprises in store: For every point on the circle there is a triangle with that point as one of the vertices that both circumscribes the ellipse and is inscribed in the circle.