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고차원 공간에서의 Poncelet-Steiner 정리

Poncelet-Steiner Theorem in Higher-Dimensional Euclidean Spaces

고차원 공간에서의 Poncelet-Steiner 정리.pdf

ABSTRACT

Georg Mohr and Lorenzo Mascheroni independently discovered that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone in 1672 and 1797 respectively. In 1822 Jean Victor Poncelet conjectured that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given, and Jakob Steiner gave a proof for it in 1833. These two theorems are called Mohr-Mascheroni theorem and Poncelet-Steiner theorem respectively.

In 2001, Bong-Gyun Koh introduced the geometric construction in higher-dimensional Euclidean spaces and proved that Mohr-Mascheroni theorem still holds in the higher-dimensional spaces.

In this paper, we prove that Steiner's construction can be established in higher-dimensional Euclidean spaces and Poncelet-Steiner theorem also holds in the spaces.

CITE THIS PAPER AS:

  • 이슬비, 고차원 공간에서의 Poncelet-Steiner 정리, 수학 나라의 앨리스 : aliceinmathland.com, 2015.
  • I Seul Bee, Poncelet-Steiner Theorem in Higher-Dimensional Euclidean Spaces, Alice in Mathematical Land: aliceinmathland.com, 2015.

If you find any errata or logical error on this paper, please contact me via designeralice AT daum.net. You can find the recent version of this paper at my personal blog: http://iseulbee.com.

References:

n차원에서의 작도(고봉균).pdf

Mascheroni and Steiner Constructions(Tom Rike).pdf

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