"퐁슬레의 정리(Poncelet's porism)"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
57번째 줄: 57번째 줄:
 
==수학용어번역==
 
==수학용어번역==
  
−
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
+
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=invariant+measure
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=invariant+measure
 
* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
 
* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
80번째 줄: 80번째 줄:
 
==관련도서==
 
==관련도서==
  
−
* [http://www.amazon.com/Poncelets-Theorem-Leopold-Flatto/dp/0821843753/ref=sr_1_2?ie=UTF8&s=books&qid=1237982324&sr=1-2 Poncelet's Theorem]<br>
+
* [http://www.amazon.com/Poncelets-Theorem-Leopold-Flatto/dp/0821843753/ref=sr_1_2?ie=UTF8&s=books&qid=1237982324&sr=1-2 Poncelet's Theorem]
 
** Leopold Flatto, American Mathematical Society (December 10, 2008)
 
** Leopold Flatto, American Mathematical Society (December 10, 2008)
−
* [http://www.amazon.com/Mathematical-Gift-Interplay-Topology-Functions/dp/0821832824 A Mathematical Gift II: The Interplay Between Topology, Functions, Geometry, and Algebra]<br>
+
* [http://www.amazon.com/Mathematical-Gift-Interplay-Topology-Functions/dp/0821832824 A Mathematical Gift II: The Interplay Between Topology, Functions, Geometry, and Algebra]
 
** Kenji Ueno, Koji Shiga, Shigeyuki Morita, Chapter 4
 
** Kenji Ueno, Koji Shiga, Shigeyuki Morita, Chapter 4
−
* [http://www.amazon.com/Mathematical-Omnibus-Lectures-Classic-Mathematics/dp/0821843168 Mathematical Omnibus: Thirty Lectures on Classic Mathematics]<br>
+
* [http://www.amazon.com/Mathematical-Omnibus-Lectures-Classic-Mathematics/dp/0821843168 Mathematical Omnibus: Thirty Lectures on Classic Mathematics]
 
** Dmitry Fuchs, Serge Tabachnikov, Chapter 8 : Lecture 29
 
** Dmitry Fuchs, Serge Tabachnikov, Chapter 8 : Lecture 29
−
* [http://www.amazon.com/Geometry-Billiards-Student-Mathematical-Library/dp/0821839195 Geometry and Billiards]<br>
+
* [http://www.amazon.com/Geometry-Billiards-Student-Mathematical-Library/dp/0821839195 Geometry and Billiards]
 
** Serge Tabachnikov
 
** Serge Tabachnikov
 
** [http://www.math.psu.edu/tabachni/Books/billiardsgeometry.pdf pdf]
 
** [http://www.math.psu.edu/tabachni/Books/billiardsgeometry.pdf pdf]
−
*  도서내검색<br>
+
*  도서내검색
 
** http://books.google.com/books?q=
 
** http://books.google.com/books?q=
 
** http://book.daum.net/search/contentSearch.do?query=
 
** http://book.daum.net/search/contentSearch.do?query=
−
*  도서검색<br>
+
*  도서검색
 
** http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
** http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
** http://book.daum.net/search/mainSearch.do?query=
 
** http://book.daum.net/search/mainSearch.do?query=
102번째 줄: 102번째 줄:
 
* http://arxiv.org/abs/1206.0163
 
* http://arxiv.org/abs/1206.0163
 
* Burskii, V. P., and A. S. Zhedanov. 2006. “On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems.” <em>Ukrainian Mathematical Journal</em> 58 (4) (April): 487-504. doi:10.1007/s11253-006-0081-x.
 
* Burskii, V. P., and A. S. Zhedanov. 2006. “On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems.” <em>Ukrainian Mathematical Journal</em> 58 (4) (April): 487-504. doi:10.1007/s11253-006-0081-x.
−
*  Bos, H. J. M. 1985. “The closure theorem of Poncelet.” <em>Rendiconti del Seminario Matematico e Fisico di Milano</em> 54 (1) (December): 145-158. doi:10.1007/BF02924855.<br>
+
*  Bos, H. J. M. 1985. “The closure theorem of Poncelet.” <em>Rendiconti del Seminario Matematico e Fisico di Milano</em> 54 (1) (December): 145-158. doi:10.1007/BF02924855.
−
* [http://dx.doi.org/10.1007/BF02567361 A poncelet theorem in space]<br>
+
* [http://dx.doi.org/10.1007/BF02567361 A poncelet theorem in space]
 
** Phillip Griffiths and Joe Harris
 
** Phillip Griffiths and Joe Harris
−
* [http://www.komal.hu/lap/2002-ang/poncelet.e.shtml Poncelet's theorem]<br>
+
* [http://www.komal.hu/lap/2002-ang/poncelet.e.shtml Poncelet's theorem]
 
** András Hraskó
 
** András Hraskó
−
* [http://dx.doi.org/10.1070/RM2006v061n06ABEH004375 A generalization of Poncelet's theorem]<br>
+
* [http://dx.doi.org/10.1070/RM2006v061n06ABEH004375 A generalization of Poncelet's theorem]
 
** V Yu Protasov, 2006 Russ. Math. Surv. 61 1180-1182
 
** V Yu Protasov, 2006 Russ. Math. Surv. 61 1180-1182
−
* [http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=2708&pf=1 Three Problems in Search of a Measure]<br>
+
* [http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=2708&pf=1 Three Problems in Search of a Measure]
 
** Jonathan King, The American Mathematics Monthly, Vol. 101 (1994), pp. 609-628.
 
** Jonathan King, The American Mathematics Monthly, Vol. 101 (1994), pp. 609-628.

2020년 11월 14일 (토) 11:14 판

개요

3128730-conics.gif

하나의 타원 C와 그 내부에 또다른 타원D가 주어져 있다.

이때 내부의 타원 D에 외접하고, 외부의 타원 C에 내접하는(*) n각형을 찾을 수 있다고 가정하자.

타원C의 임의의 점을 꼭지점으로 갖는, 같은 성질을 갖는 n각형이 존재한다.

즉 (*)의 성질을 갖는 하나의 n각형이 존재하면, 그러한 n각형이 무한히 많이 존재한다.

 

  • 위 그림의 경우는 삼각형의 경우
  • Poncelet's theorem 또는 Poncelet's porism 으로 불림

 

 

타원곡선의 군 구조를 이용한 증명

 

 

불변측도(invariant measure)의 존재를 이용한 증명

 

 

 

재미있는 사실

  • 감옥에 있던 퐁슬레 수학 공부한 사연

 

 

 

 

관련된 항목들

 

 

수학용어번역

 

 

사전형태의 자료

 

 

 

관련도서

 

관련논문

원본 주소 "https://wiki.mathnt.net/index.php?title=퐁슬레의_정리(Poncelet%27s_porism)&oldid=44415"