"비에타의 공식"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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(사용자 2명의 중간 판 21개는 보이지 않습니다) | |||
1번째 줄: | 1번째 줄: | ||
− | + | ==이 항목의 스프링노트 원문주소== | |
− | + | * [[비에타의 공식]] | |
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− | + | ==개요== | |
− | + | * 파이에 대한 무한곱 표현 | |
+ | * François Viète에 의해 발견:<math>\frac{2}{\pi}=\frac{\sqrt{2}}{2}\frac{\sqrt{2+\sqrt{2}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}{2}\cdots</math> | ||
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− | < | + | <math>\frac{2}{\pi }=\frac{\sqrt{2}}{2}\frac{\sqrt{2+\sqrt{2}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}}{2}</math> |
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+ | ==재미있는 사실== | ||
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* 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query= | * 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
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− | + | ==역사== | |
− | + | * 1579년? 1593년 발견 | |
+ | * [http://www.google.com/search?hl=en&tbs=tl:1&q=Viete%27s+formula http://www.google.com/search?hl=en&tbs=tl:1&q=Viete's+formula] | ||
+ | * [[수학사 연표]] | ||
+ | * | ||
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− | + | ==메모== | |
− | + | * http://www.leejeonghwan.com/cgi-bin/read.cgi?board=express&y_number=2&nnew=2 | |
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− | + | ==관련된 항목들== | |
* [[nested radicals]] | * [[nested radicals]] | ||
* [[삼각함수]] | * [[삼각함수]] | ||
+ | * [[월리스 곱 (Wallis product formula)]] | ||
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− | + | ==수학용어번역== | |
* http://www.google.com/dictionary?langpair=en|ko&q= | * http://www.google.com/dictionary?langpair=en|ko&q= | ||
− | * [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=&fstr= 대한수학회 수학 학술 용어집] |
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ||
− | * [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 | + | * [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] |
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− | + | ==사전 형태의 자료== | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
+ | * [http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formula http://en.wikipedia.org/wiki/Viète's_formula] | ||
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | ||
− | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
** http://www.research.att.com/~njas/sequences/?q= | ** http://www.research.att.com/~njas/sequences/?q= | ||
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− | + | ==관련논문== | |
− | * [http://www.jstor.org/stable/2589027 The Union of Vieta's and Wallis's Products for Pi] | + | * [http://www.jstor.org/stable/2589027 The Union of Vieta's and Wallis's Products for Pi] |
** Thomas J. Osler, The American Mathematical Monthly, Vol. 106, No. 8 (Oct., 1999), pp. 774-776 | ** Thomas J. Osler, The American Mathematical Monthly, Vol. 106, No. 8 (Oct., 1999), pp. 774-776 | ||
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
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− | + | ==블로그== | |
* 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q= | * 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q= | ||
− | + | [[분류:원주율]] | |
− | * | + | |
− | + | ==메타데이터== | |
− | * [ | + | ===위키데이터=== |
+ | * ID : [https://www.wikidata.org/wiki/Q949597 Q949597] | ||
+ | ===Spacy 패턴 목록=== | ||
+ | * [{'LOWER': 'viète'}, {'LOWER': "'s"}, {'LEMMA': 'formula'}] |
2021년 2월 17일 (수) 05:46 기준 최신판
이 항목의 스프링노트 원문주소
개요
- 파이에 대한 무한곱 표현
- François Viète에 의해 발견\[\frac{2}{\pi}=\frac{\sqrt{2}}{2}\frac{\sqrt{2+\sqrt{2}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}{2}\cdots\]
\(\frac{2}{\pi }=\frac{\sqrt{2}}{2}\frac{\sqrt{2+\sqrt{2}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}{2}\frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}}{2}\)
재미있는 사실
역사
- 1579년? 1593년 발견
- http://www.google.com/search?hl=en&tbs=tl:1&q=Viete's+formula
- 수학사 연표
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Viète's_formula
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- The Union of Vieta's and Wallis's Products for Pi
- Thomas J. Osler, The American Mathematical Monthly, Vol. 106, No. 8 (Oct., 1999), pp. 774-776
- http://www.jstor.org/action/doBasicSearch?Query=
- http://dx.doi.org/
블로그
메타데이터
위키데이터
- ID : Q949597
Spacy 패턴 목록
- [{'LOWER': 'viète'}, {'LOWER': "'s"}, {'LEMMA': 'formula'}]