早期關於Poncelet's Porism的研究是一個兩圓與三角形的公式.之後的發展推廣到多邊形與兩圓的研究.另一個重要里程則是推廣到兩圓錐曲線與多邊形的研究.

Abstract

The prehistory of Poncelet’s Porism is connected with a special formula (Chapple’s formula) from the geometry of the triangle. During the prehistory of the Poncelet theorem some mathematicians made this formula explicitly and formulated the closure theorem as a consequence. In 1746, Chapple considered triangle and two circles. In 1797, Fuss studied quadrilateral and two circles. With a sequel article [1802] he studied 5, 6, 7 and 8 gons and two circles. Poncelet found and proved the closure theorem in 1813-14 and published it in 1822. In 1827, Steiner as did 3, 4, 5, 6, 8 gons and two circles. Some year after Poncelet, Jacobi [1828] was aware that these results can be generalized to conics but he did not work out this generalization as far as possible. Many mathematicians have taken up Jacobi’s results and developed them further. [Loria 1889] [Dingeldey 1903] [Koetter 1901] [Chauny 1923] [Kerawala 1947] [Doerrie 1965] [Griffiths, Harris 1978]

This paper presents the design of Poncelet’s Porism under Cabri2D, 3D Geometry, interactive dynamic software of geometry. It is divided into six sections. You can see the detail clearly in the website:
http://oz.nthu.edu.tw/~g923261/indexa1.htm
Here anyone can see my achievement easily and application of 2D, 3D dynamic geometry.

Reference

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