"라마누잔(1887- 1920)"의 두 판 사이의 차이

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<h5>이 항목의 스프링노트 원문주소</h5>
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==개요==
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* [[라마누잔(1887- 1920)]]
 
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<h5>개요</h5>
 
  
 
* 인도의 수학자
 
* 인도의 수학자
13번째 줄: 5번째 줄:
 
* 수많은 기묘한 공식들을 많이 남김.
 
* 수많은 기묘한 공식들을 많이 남김.
  
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<h5>라마누잔과 파이</h5>
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==라마누잔과 파이==
  
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* [[라마누잔과 파이]] 항목에서 다룸<br><math>\frac{1}{\pi}= \frac{2\sqrt2}{9801}\sum_{n=0}^{\infty}\frac{(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}</math>[[라마누잔과 파이|]]<br>
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* [[라마누잔과 파이]] 항목에서 다룸<br><math>\frac{1}{\pi}= \frac{2\sqrt2}{9801}\sum_{n=0}^{\infty}\frac{(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}</math>[[라마누잔과 파이|라마누잔과 파이]]<br>
  
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<h5>nested radicals</h5>
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==nested radicals==
  
 
* [[nested radicals]]<br><math>\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+6\cdots}}}}} = 3</math><br>
 
* [[nested radicals]]<br><math>\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+6\cdots}}}}} = 3</math><br>
  
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<h5>라마누잔 연분수</h5>
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==라마누잔 연분수==
  
 
* [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]] 항목에서 다룸<br><math>\cfrac{1}{1 + \cfrac{e^{-2\pi}}{1 + \cfrac{e^{-4\pi}}{1+\dots}}} = \left({\sqrt{5+\sqrt{5}\over 2}-{\sqrt{5}+1\over 2}}\right)e^{2\pi/5} = e^{2\pi/5}\left({\sqrt{\varphi\sqrt{5}}-\varphi}\right) = 0.9981360\dots</math><br>
 
* [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]] 항목에서 다룸<br><math>\cfrac{1}{1 + \cfrac{e^{-2\pi}}{1 + \cfrac{e^{-4\pi}}{1+\dots}}} = \left({\sqrt{5+\sqrt{5}\over 2}-{\sqrt{5}+1\over 2}}\right)e^{2\pi/5} = e^{2\pi/5}\left({\sqrt{\varphi\sqrt{5}}-\varphi}\right) = 0.9981360\dots</math><br>
  
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<h5>타원적분의 singular values</h5>
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==타원적분의 singular values==
  
 
* [[라마누잔(1887- 1920)|라마누잔]]이 하디에게 보낸 1913년의 편지에는 다음이 수록<br><math>k_{210}=\left(-1+\sqrt{2}\right)^2 \left(2-\sqrt{3}\right) \left(8-3 \sqrt{7}\right) \left(-\sqrt{6}+\sqrt{7}\right)^2 \left(-3+\sqrt{10}\right)^2 \left(4-\sqrt{15}\right)^2 \left(-\sqrt{14}+\sqrt{15}\right) \left(6-\sqrt{35}\right)</math><br>
 
* [[라마누잔(1887- 1920)|라마누잔]]이 하디에게 보낸 1913년의 편지에는 다음이 수록<br><math>k_{210}=\left(-1+\sqrt{2}\right)^2 \left(2-\sqrt{3}\right) \left(8-3 \sqrt{7}\right) \left(-\sqrt{6}+\sqrt{7}\right)^2 \left(-3+\sqrt{10}\right)^2 \left(4-\sqrt{15}\right)^2 \left(-\sqrt{14}+\sqrt{15}\right) \left(6-\sqrt{35}\right)</math><br>
47번째 줄: 39번째 줄:
 
* [[타원적분의 singular value k]]
 
* [[타원적분의 singular value k]]
  
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<h5>메모</h5>
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==메모==
  
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* http://dspace.rri.res.in/bitstream/2289/741/1/1990%20CS%20V59%20%20p1309.pdf
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* http://dspace.rri.res.in/bitstream/2289/741/1/1990%20 CS %20 V59 %20 %20 p1309.pdf
 
* [http://www.theartsdesk.com/index.php?option=com_k2&view=item&id=2165:the-mozart-and-salieri-of-maths&Itemid=29 Complicite and the Mozart and Salieri of Maths]
 
* [http://www.theartsdesk.com/index.php?option=com_k2&view=item&id=2165:the-mozart-and-salieri-of-maths&Itemid=29 Complicite and the Mozart and Salieri of Maths]
 
* http://www.youtube.com/watch?v=OARGZ1xXCxs
 
* http://www.youtube.com/watch?v=OARGZ1xXCxs
  
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<h5>연대기</h5>
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==연대기==
  
 
* 1887년 12월 출생
 
* 1887년 12월 출생
70번째 줄: 62번째 줄:
 
* [[수학사연표 (역사)|수학사연표]]
 
* [[수학사연표 (역사)|수학사연표]]
  
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<h5>관련된 고교수학 또는 대학수학</h5>
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==관련된 고교수학 또는 대학수학==
  
 
* [[복소함수론]]
 
* [[복소함수론]]
81번째 줄: 73번째 줄:
 
* [[이차형식]]
 
* [[이차형식]]
  
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<h5>관련된 항목들</h5>
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==관련된 항목들==
  
 
* [[라마누잔의 class invariants]]
 
* [[라마누잔의 class invariants]]
 
* [[nested radicals]]<br>
 
* [[nested radicals]]<br>
 
* [[라마누잔과 1729]]<br>
 
* [[라마누잔과 1729]]<br>
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* [[라마누잔과 파이]][[로저스-라마누잔 항등식|]]
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* [[라마누잔과 파이]][[로저스-라마누잔 항등식|로저스-라마누잔 항등식]]
 
* [[분할수의 근사 공식 (하디-라마누잔-라데마커 공식)|하디-라마누잔 분할수 공식]]
 
* [[분할수의 근사 공식 (하디-라마누잔-라데마커 공식)|하디-라마누잔 분할수 공식]]
 
* [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]]
 
* [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]]
100번째 줄: 92번째 줄:
 
* [[판별식 (discriminant) 함수와 라마누잔의 타우 함수(tau function)|판별식 (discriminant) 함수]]
 
* [[판별식 (discriminant) 함수와 라마누잔의 타우 함수(tau function)|판별식 (discriminant) 함수]]
  
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">사전 형태의 자료</h5>
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==사전 형태의 자료==
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
113번째 줄: 105번째 줄:
 
** http://www.research.att.com/~njas/sequences/?q=
 
** http://www.research.att.com/~njas/sequences/?q=
  
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<h5>관련도서 및 추천도서</h5>
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==관련도서==
  
 
* [http://www.yes24.com/Goods/FTGoodsView.aspx?goodsNo=103183&CategoryNumber=001001002015001 수학이 나를 불렀다]<br>
 
* [http://www.yes24.com/Goods/FTGoodsView.aspx?goodsNo=103183&CategoryNumber=001001002015001 수학이 나를 불렀다]<br>
125번째 줄: 117번째 줄:
 
* [http://www.amazon.com/Number-Theory-Spirit-Ramanujan-Berndt/dp/0821841785 Number Theory in the Spirit of Ramanujan]<br>
 
* [http://www.amazon.com/Number-Theory-Spirit-Ramanujan-Berndt/dp/0821841785 Number Theory in the Spirit of Ramanujan]<br>
 
** Bruce C. Berndt
 
** Bruce C. Berndt
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* [http://www.amazon.com/Ramanujans-Notebooks-Bruce-C-Berndt/dp/0387961100/ref=pd_sim_b_3 Ramanujan's Notebooks]: I,II,III,IV,V<br>
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* [http://www.amazon.com/Ramanujans-Notebooks-Bruce-C-Berndt/dp/0387961100/ref=pd_sim _b _ 3 Ramanujan's Notebooks]: I,II,III,IV,V<br>
 
** Bruce C. Berndt
 
** Bruce C. Berndt
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* [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/038725529X/ref=pd_sim_b_2 Ramanujan's Lost Notebook] : I, [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/0387777652/ref=pd_sim_b_3 II]<br>
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* [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/038725529X/ref=pd_sim _b _ 2 Ramanujan's Lost Notebook] : I, [http://www.amazon.com/Ramanujans-Lost-Notebook-Part-Pt/dp/0387777652/ref=pd_sim _b _ 3 II]<br>
 
** George E. Andrews and Bruce C. Berndt
 
** George E. Andrews and Bruce C. Berndt
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* Ramanujan revisited : proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1-5, 1987 / edited by George E. Andrews ... [et al.].<1988>  Ramanujan Centenary Conference (1987 : University of Illinois at Urbana-Champaign), Boston : Academic Press, c1988.
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* Ramanujan revisited : proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1-5, 1987 / edited by George E. Andrews ... [et al.].<1988> Ramanujan Centenary Conference (1987 : University of Illinois at Urbana-Champaign), Boston : Academic Press, c1988.
 
* Collected papers of Srinivasa Ramanujan, edited by G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, Cambridge [Eng.] The University Press, 1927.
 
* Collected papers of Srinivasa Ramanujan, edited by G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, Cambridge [Eng.] The University Press, 1927.
 
*  도서내검색<br>
 
*  도서내검색<br>
135번째 줄: 127번째 줄:
 
** http://book.daum.net/search/contentSearch.do?query=
 
** http://book.daum.net/search/contentSearch.do?query=
 
*  도서검색<br>
 
*  도서검색<br>
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** http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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** http://www.amazon.com/s/ref=nb_ss _gw?url=search-alias %3 Dstripbooks&field-keywords=
 
** http://book.daum.net/search/mainSearch.do?query=
 
** http://book.daum.net/search/mainSearch.do?query=
  
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<h5>관련논문</h5>
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==관련논문==
  
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* Atle Selberg [http://www.ias.ac.in/resonance/Dec1996/pdf/Dec1996Reflections.pdf Reflections around the Ramanujan centenary], December 1996
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* Atle Selberg [http://www.ias.ac.in/resonance/Dec1996/pdf/Dec1996Reflections.pdf Reflections around the Ramanujan centenary], December 1996
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* George E. Andrews and Bruce C. Berndt [http://www.ams.org/notices/200801/tx080100018p.pdf Your hit parade: The top ten most fascinating formulas from Ramanujan's Lost Notebook], <em style="">Notices Amer. Math. Soc.</em>, 55 (No. 1, Jan. 2008), 18-30
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* George E. Andrews and Bruce C. Berndt [http://www.ams.org/notices/200801/tx080100018p.pdf Your hit parade: The top ten most fascinating formulas from Ramanujan's Lost Notebook], <em style="">Notices Amer. Math. Soc.</em>, 55 (No. 1, Jan. 2008), 18-30
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* Bruce C. Berndt, [http://www.jstor.org/stable/2689995 Ramanujan's Notebooks] <cite>Mathematics Magazine</cite>, Vol. 51, No. 3 (May, 1978), pp. 147-164
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* Bruce C. Berndt, [http://www.jstor.org/stable/2689995 Ramanujan's Notebooks] <cite>Mathematics Magazine</cite>, Vol. 51, No. 3 (May, 1978), pp. 147-164
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* George E. Andrews, [http://www.jstor.org/stable/2321943 An Introduction to Ramanujan's "lost" Notebook]<cite>The American Mathematical Monthly</cite>, Vol. 86, No. 2 (Feb., 1979), pp. 89-108
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* George E. Andrews, [http://www.jstor.org/stable/2321943 An Introduction to Ramanujan's "lost" Notebook]<cite>The American Mathematical Monthly</cite>, Vol. 86, No. 2 (Feb., 1979), pp. 89-108
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* George E. Andrews, [http://www.jstor.org/stable/2974472 Simplicity and Surprise in Ramanujan's "Lost" Notebook] <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 10 (Dec., 1997), pp. 918-925
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* George E. Andrews, [http://www.jstor.org/stable/2974472 Simplicity and Surprise in Ramanujan's "Lost" Notebook] <cite>The American Mathematical Monthly</cite>, Vol. 104, No. 10 (Dec., 1997), pp. 918-925
 
* [http://www.jstor.org/stable/2974471 Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists]<cite>The American Mathematical Monthly</cite>, Vol. 104, No. 10 (Dec., 1997), pp. 912-917
 
* [http://www.jstor.org/stable/2974471 Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists]<cite>The American Mathematical Monthly</cite>, Vol. 104, No. 10 (Dec., 1997), pp. 912-917
 
* [http://www.jstor.org/stable/2323885 Ramanujan--For Lowbrows]<br>
 
* [http://www.jstor.org/stable/2323885 Ramanujan--For Lowbrows]<br>
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** Bruce C. Berndt and S. Bhargava, <cite>The American Mathematical Monthly</cite>, Vol. 100, No. 7 (Aug. - Sep., 1993), pp. 644-656
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** Bruce C. Berndt and S. Bhargava, <cite>The American Mathematical Monthly</cite>, Vol. 100, No. 7 (Aug. - Sep., 1993), pp. 644-656
 
* [http://dx.doi.org/10.1070/RM1990v045n01ABEH002325 Ramanujan and hypergeometric and basic hypergeometric series]<br>
 
* [http://dx.doi.org/10.1070/RM1990v045n01ABEH002325 Ramanujan and hypergeometric and basic hypergeometric series]<br>
 
** R Askey 1990 Russ. Math. Surv. 45 37-86
 
** R Askey 1990 Russ. Math. Surv. 45 37-86
158번째 줄: 150번째 줄:
 
** Richard Askey, <cite>The American Mathematical Monthly</cite>, Vol. 87, No. 5 (May, 1980), pp. 346-359
 
** Richard Askey, <cite>The American Mathematical Monthly</cite>, Vol. 87, No. 5 (May, 1980), pp. 346-359
 
* [http://www.jstor.org/stable/2301659 The Indian Mathematician Ramanujan]<br>
 
* [http://www.jstor.org/stable/2301659 The Indian Mathematician Ramanujan]<br>
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** G. H. Hardy, <cite>The American Mathematical Monthly</cite>, Vol. 44, No. 3 (Mar., 1937), pp. 137-155
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** G. H. Hardy, <cite>The American Mathematical Monthly</cite>, Vol. 44, No. 3 (Mar., 1937), pp. 137-155
  
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* [http://www.jstor.org/stable/2311980 The Nonvanishing of Ramanujan's τ-Function]<br>
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* [http://www.jstor.org/stable/2311980 The Nonvanishing of Ramanujan's \[Tau]-Function]<br>
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** J. M. Gandhi, <cite>The American Mathematical Monthly</cite>, Vol. 68, No. 8 (Oct., 1961), pp. 757-760
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** J. M. Gandhi, <cite>The American Mathematical Monthly</cite>, Vol. 68, No. 8 (Oct., 1961), pp. 757-760
  
 
* [http://www.jstor.org/stable/2299066 The Development of "Partitio Numerorum," with Particular Reference to the Work of Messrs. Hardy, Littlewood and Ramanujan]<br>
 
* [http://www.jstor.org/stable/2299066 The Development of "Partitio Numerorum," with Particular Reference to the Work of Messrs. Hardy, Littlewood and Ramanujan]<br>
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** Aubrey J. Kempner, <cite>The American Mathematical Monthly</cite>, Vol. 30, No. 7 (Nov., 1923), pp. 354-369
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** Aubrey J. Kempner, <cite>The American Mathematical Monthly</cite>, Vol. 30, No. 7 (Nov., 1923), pp. 354-369
  
 
* [http://www.jstor.org/stable/2298749 The Development of "Partitio Numerorum," with Particular Reference to the Work of Messrs. Hardy, Littlewood and Ramanujan]<br>
 
* [http://www.jstor.org/stable/2298749 The Development of "Partitio Numerorum," with Particular Reference to the Work of Messrs. Hardy, Littlewood and Ramanujan]<br>
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** Aubrey J. Kempner, <cite>The American Mathematical Monthly</cite>, Vol. 30, No. 8 (Dec., 1923), pp. 416-425
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** Aubrey J. Kempner, <cite>The American Mathematical Monthly</cite>, Vol. 30, No. 8 (Dec., 1923), pp. 416-425
  
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<h5>관련링크 및 웹페이지</h5>
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==관련링크 및 웹페이지==
  
 
*  Bruce Berndt 교수의 홈페이지<br>
 
*  Bruce Berndt 교수의 홈페이지<br>
181번째 줄: 173번째 줄:
 
* [http://www.geocities.com/titus_piezas/ramanujan.html The Ramanujan Pages] by Titus Piezas III
 
* [http://www.geocities.com/titus_piezas/ramanujan.html The Ramanujan Pages] by Titus Piezas III
  
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<h5>관련기사</h5>
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==관련기사==
  
 
* http://www.hani.co.kr/arti/science/kistiscience/365931.html
 
* http://www.hani.co.kr/arti/science/kistiscience/365931.html
 
*  네이버 뉴스 검색 (키워드 수정)<br>
 
*  네이버 뉴스 검색 (키워드 수정)<br>
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** [http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=%EB%9D%BC%EB%A7%88%EB%88%84%EC%9E%94 http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=라마누잔]
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** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=라마누잔]
 
** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

2012년 10월 14일 (일) 15:29 판

개요

  • 인도의 수학자
  • 공식적인 수학교육이 거의 없는 상태에서 스스로 수학지식을 습득
  • 수많은 기묘한 공식들을 많이 남김.



라마누잔과 파이



nested radicals

  • nested radicals
    \(\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+6\cdots}}}}} = 3\)



라마누잔 연분수

  • 로저스-라마누잔 연분수와 항등식 항목에서 다룸
    \(\cfrac{1}{1 + \cfrac{e^{-2\pi}}{1 + \cfrac{e^{-4\pi}}{1+\dots}}} = \left({\sqrt{5+\sqrt{5}\over 2}-{\sqrt{5}+1\over 2}}\right)e^{2\pi/5} = e^{2\pi/5}\left({\sqrt{\varphi\sqrt{5}}-\varphi}\right) = 0.9981360\dots\)



타원적분의 singular values

  • 라마누잔이 하디에게 보낸 1913년의 편지에는 다음이 수록
    \(k_{210}=\left(-1+\sqrt{2}\right)^2 \left(2-\sqrt{3}\right) \left(8-3 \sqrt{7}\right) \left(-\sqrt{6}+\sqrt{7}\right)^2 \left(-3+\sqrt{10}\right)^2 \left(4-\sqrt{15}\right)^2 \left(-\sqrt{14}+\sqrt{15}\right) \left(6-\sqrt{35}\right)\)



메모


연대기

  • 1887년 12월 출생
  • 대학에서 두번 쫓겨남
  • 1913년 하디에게 편지
  • 캠브리지에서 하디와 공동작업
  • 1919년 인도로 돌아감
  • 1920년 1월 12일자, 하디에게 보낸 마지막 편지
  • 1920년 4월 사망 (32세)
  • 수학사연표



관련된 고교수학 또는 대학수학



관련된 항목들



사전 형태의 자료



관련도서



관련논문




관련링크 및 웹페이지



관련기사

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