"삼각함수의 역사"의 두 판 사이의 차이

수학노트
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잔글 (찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로)
 
(같은 사용자의 중간 판 6개는 보이지 않습니다)
1번째 줄: 1번째 줄:
==이 항목의 스프링노트 원문주소==
 
 
* [[삼각함수의 역사]]
 
 
 
 
 
 
 
 
 
==개요==
 
==개요==
  
13번째 줄: 5번째 줄:
 
* [http://nrich.maths.org/6908&part= History of Trigonometry Part 3]
 
* [http://nrich.maths.org/6908&part= History of Trigonometry Part 3]
  
 
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==삼각함수 표의 역사==
 
==삼각함수 표의 역사==
  
 
* [http://www.wolframalpha.com/input/?i=sin%28pi/180%29+in+base+60 http://www.wolframalpha.com/input/?i=sin(pi/180)+in+base+60]
 
* [http://www.wolframalpha.com/input/?i=sin%28pi/180%29+in+base+60 http://www.wolframalpha.com/input/?i=sin(pi/180)+in+base+60]
*  http://www.ams.org/journals/mcom/1943-01-002/<br>
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*  http://www.ams.org/journals/mcom/1943-01-002/
 
** http://www.ams.org/journals/mcom/1943-01-002/S0025-5718-43-99135-5/S0025-5718-43-99135-5.pdf
 
** http://www.ams.org/journals/mcom/1943-01-002/S0025-5718-43-99135-5/S0025-5718-43-99135-5.pdf
 
* http://www.amazon.com/Episodes-History-Mathematics-Mathematical-Library/dp/0883856131
 
* http://www.amazon.com/Episodes-History-Mathematics-Mathematical-Library/dp/0883856131
  
 
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==표만들기 기술==
 
==표만들기 기술==
  
* [http://en.wikipedia.org/wiki/Exact_trigonometric_constants ]http://en.wikipedia.org/wiki/Exact_trigonometric_constants
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* http://en.wikipedia.org/wiki/Exact_trigonometric_constants
 
* [[삼각함수의 값]]
 
* [[삼각함수의 값]]
  
 
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==톨레미 '알마게스트'==
 
==톨레미 '알마게스트'==
  
 
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==인도의 삼각함수==
 
==인도의 삼각함수==
49번째 줄: 41번째 줄:
 
* http://en.wikipedia.org/wiki/Aryabhata%27s_sine_table
 
* http://en.wikipedia.org/wiki/Aryabhata%27s_sine_table
 
* http://en.wikipedia.org/wiki/Madhava%27s_sine_table
 
* http://en.wikipedia.org/wiki/Madhava%27s_sine_table
*  Hayashi, Takao. 1997. Aryabhaa's Rule and Table for Sine-Differences. Historia Mathematica 24, no. 4 (November): 396-406. doi:[http://dx.doi.org/10.1006/hmat.1997.2160 10.1006/hmat.1997.2160].<br>
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*  Hayashi, Takao. 1997. Aryabhaa's Rule and Table for Sine-Differences. Historia Mathematica 24, no. 4 (November): 396-406. doi:[http://dx.doi.org/10.1006/hmat.1997.2160 10.1006/hmat.1997.2160].
  
 
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==이슬람에서의 발전==
 
==이슬람에서의 발전==
  
 
* [http://www.springerlink.com/content/cvj58f7r80yl166f/ Al-Khwārizmī's Sine Tables and a Western Table with the Hindu Norm of R = 150]
 
* [http://www.springerlink.com/content/cvj58f7r80yl166f/ Al-Khwārizmī's Sine Tables and a Western Table with the Hindu Norm of R = 150]
*  Al-Biruni 의 업적<br>
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*  Al-Biruni 의 업적
 
** [http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko&ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko][http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko&ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false]
 
** [http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko&ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko][http://books.google.com/books?id=s7JoNDSA9zAC&pg=PA66&lpg=PA66&dq=al+biruni+exhaustive+study+shadow&source=bl&ots=45JILsceTk&sig=3Mu92wU-g3YMeZINhEKfWndeILA&hl=ko&ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false ei=ewYyTfO0Oo2CsQOztMnQBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false]
 
** Muḥammad ibn Aḥmad Bīrūnī and Edward Stewart Kennedy, The exhaustive treatise on shadows (Institute for the History of Arabic Science, University of Aleppo, 1976).
 
** Muḥammad ibn Aḥmad Bīrūnī and Edward Stewart Kennedy, The exhaustive treatise on shadows (Institute for the History of Arabic Science, University of Aleppo, 1976).
66번째 줄: 58번째 줄:
 
* http://en.wikipedia.org/wiki/Geography_and_cartography_in_the_Caliphate
 
* http://en.wikipedia.org/wiki/Geography_and_cartography_in_the_Caliphate
  
 
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==동아시아의 삼각함수==
 
==동아시아의 삼각함수==
74번째 줄: 66번째 줄:
 
* [[한국의 수학]][http://www.wolframalpha.com/input/?i=sin+%28pi*%2825%2B42/60%2B51/3600%29/180%29 http://www.wolframalpha.com/input/?i=sin+(pi*(25%2B42/60%2B51/3600)/180)]
 
* [[한국의 수학]][http://www.wolframalpha.com/input/?i=sin+%28pi*%2825%2B42/60%2B51/3600%29/180%29 http://www.wolframalpha.com/input/?i=sin+(pi*(25%2B42/60%2B51/3600)/180)]
  
 
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==유럽의 삼각함수==
 
==유럽의 삼각함수==
  
*  레기오몬타누스<br>
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*  레기오몬타누스
 
** http://www.hps.cam.ac.uk/starry/regiotables.html
 
** http://www.hps.cam.ac.uk/starry/regiotables.html
  
89번째 줄: 81번째 줄:
 
* 피티스쿠스
 
* 피티스쿠스
  
 
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==푸리에==
 
==푸리에==
97번째 줄: 89번째 줄:
 
* 1807
 
* 1807
  
 
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==연표==
 
==연표==
108번째 줄: 100번째 줄:
 
* 1693년 라이프니츠 조화진동자의 급수해, 다음해 요한 베르누이 역시 급수해로 만족
 
* 1693년 라이프니츠 조화진동자의 급수해, 다음해 요한 베르누이 역시 급수해로 만족
 
* 1696년부터 1730년대까지 다양한 미적분학 교과서가 출판되지만 삼각함수의 미적분학은 등장하지 않음
 
* 1696년부터 1730년대까지 다양한 미적분학 교과서가 출판되지만 삼각함수의 미적분학은 등장하지 않음
*  1939년 오일러 '새로운 형태의 진동에 대하여(De novo genere oscillatonum)' 출판 [http://www.math.dartmouth.edu/%7Eeuler/pages/E126.html http://www.math.dartmouth.edu/~euler/pages/E126.html]<br>
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*  1939년 오일러 '새로운 형태의 진동에 대하여(De novo genere oscillatonum)' 출판 [http://www.math.dartmouth.edu/%7Eeuler/pages/E126.html http://www.math.dartmouth.edu/~euler/pages/E126.html]
 
** [[오일러(1707-1783)]]
 
** [[오일러(1707-1783)]]
 
* 1965년 4월 쿨리와 투키의 논문이 출판
 
* 1965년 4월 쿨리와 투키의 논문이 출판
114번째 줄: 106번째 줄:
 
* [http://jeff560.tripod.com/mathword.html Earliest Known Uses of Some of the Words of Mathematics]
 
* [http://jeff560.tripod.com/mathword.html Earliest Known Uses of Some of the Words of Mathematics]
 
* [http://jeff560.tripod.com/mathsym.html Earliest Uses of Various Mathematical Symbols]
 
* [http://jeff560.tripod.com/mathsym.html Earliest Uses of Various Mathematical Symbols]
* [[수학사연표 (역사)|수학사연표]]
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* [[수학사 연표]]
  
 
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==메모==
 
==메모==
131번째 줄: 123번째 줄:
 
While many new aspects of trigonometry were being discovered, the chord, sine, versine and cosine were developed in the investigation of astronomical problems, and conceived of as properties of angles at the centre of the heavenly sphere. In contrast, tangent and cotangent properties were derived from the measurement of shadows of a gnomon and the problems of telling the time. http://nrich.maths.org/6908&part=
 
While many new aspects of trigonometry were being discovered, the chord, sine, versine and cosine were developed in the investigation of astronomical problems, and conceived of as properties of angles at the centre of the heavenly sphere. In contrast, tangent and cotangent properties were derived from the measurement of shadows of a gnomon and the problems of telling the time. http://nrich.maths.org/6908&part=
  
 
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The sine formula for spherical triangleswas used to good effect by the famous Islamic scholar al-B¯ır¯un¯ı with his solution to the qibla problem, this being to<br> determine the direction in which Mecca was closest from a given location on the Earth, i.e. along a great circle
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The sine formula for spherical triangleswas used to good effect by the famous Islamic scholar al-B¯ır¯un¯ı with his solution to the qibla problem, this being to determine the direction in which Mecca was closest from a given location on the Earth, i.e. along a great circle
  
 
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시간과 주기운동 http://en.wikipedia.org/wiki/Atomic_clock
 
시간과 주기운동 http://en.wikipedia.org/wiki/Atomic_clock
147번째 줄: 139번째 줄:
 
시계종류 : sundial, water, divisional time, pendulum, quartz, atomic clock http://www.youtube.com/watch?v=4T8uyD0AvzI
 
시계종류 : sundial, water, divisional time, pendulum, quartz, atomic clock http://www.youtube.com/watch?v=4T8uyD0AvzI
  
 
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==관련된 항목들==
 
==관련된 항목들==
155번째 줄: 147번째 줄:
 
* [[뉴딜과 mathematical tables project |뉴딜과 mathematical tables project]]
 
* [[뉴딜과 mathematical tables project |뉴딜과 mathematical tables project]]
  
 
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==수학용어번역==
 
==수학용어번역==
  
* 단어사전 [http://www.google.com/dictionary?langpair=en%7Cko&q=palatinum http://www.google.com/dictionary?langpair=en|ko&q=palatinum]
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* 단어사전 [http://www.google.com/dictionary?langpair=en%7Cko&q=palatinum http://www.google.com/dictionary?langpair=en|ko&q=palatinum]
* 발음사전 http://www.forvo.com/search/
 
* [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=eng_term&fstr=
 
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
 
* [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==
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==사전 형태의 자료==
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
 
* [http://en.wikipedia.org/wiki/Almagest ]http://en.wikipedia.org/wiki/Almagest
 
* [http://en.wikipedia.org/wiki/Almagest ]http://en.wikipedia.org/wiki/Almagest
* http://en.wikipedia.org/wiki/Hipparchus<br>
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* http://en.wikipedia.org/wiki/Hipparchus
* http://en.wikipedia.org/wiki/
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* http://www.proofwiki.org/wiki/
 
* http://www.wolframalpha.com/input/?i=
 
* [http://eom.springer.de/default.htm The Online Encyclopaedia of Mathematics]
 
* [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]
 
 
 
 
 
 
 
 
 
  
 
==관련논문==
 
==관련논문==
  
*  MOUSSA, ALI. 2010. The Trigonometric Functions, as They Were in the Arabic-Islamic Civilization. Arabic Sciences and Philosophy 20, no. 01: 93-104. doi:[http://dx.doi.org/10.1017/S0957423909990099 10.1017/S0957423909990099]. <br>  <br>  <br>
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*  MOUSSA, ALI. 2010. The Trigonometric Functions, as They Were in the Arabic-Islamic Civilization. Arabic Sciences and Philosophy 20, no. 01: 93-104. doi:[http://dx.doi.org/10.1017/S0957423909990099 10.1017/S0957423909990099].    
 
* [http://www.math.usma.edu/people/rickey/talks/06-10-13-Marist-trig/06-10-13-trig.pdf Some History of the Calculus of the Trigonometric Functions]
 
* [http://www.math.usma.edu/people/rickey/talks/06-10-13-Marist-trig/06-10-13-trig.pdf Some History of the Calculus of the Trigonometric Functions]
* [http://dx.doi.org/10.1007/1-4020-2204-2_16 A Note on the History of Trigonometric Functions]<br>
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* [http://dx.doi.org/10.1007/1-4020-2204-2_16 A Note on the History of Trigonometric Functions]
 
** Jean-Pierre Merlet, 2004, 5, 195-200
 
** Jean-Pierre Merlet, 2004, 5, 195-200
 
* Katz, Victor J., “The curious history of trigonometry,” The UMAP Journal, 11 (1990), 339–354.
 
* Katz, Victor J., “The curious history of trigonometry,” The UMAP Journal, 11 (1990), 339–354.
198번째 줄: 175번째 줄:
 
* Boyer, C., 1947. History of the derivative and integral of the sine. Mathematics Teacher 40, pp. 267–275.
 
* Boyer, C., 1947. History of the derivative and integral of the sine. Mathematics Teacher 40, pp. 267–275.
 
* [http://www-gap.cs.st-and.ac.uk/%7Ehistory/HistTopics/References/Trigonometric_functions.html References for: The trigonometric functions]
 
* [http://www-gap.cs.st-and.ac.uk/%7Ehistory/HistTopics/References/Trigonometric_functions.html References for: The trigonometric functions]
* http://www.jstor.org/action/doBasicSearch?Query=
 
* http://www.ams.org/mathscinet
 
* http://dx.doi.org/10.1007/1-4020-2204-2_16
 
  
 
 
  
 
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==관련도서==
 
==관련도서==
  
 
* Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (Princeton University Press, 2009).
 
* Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (Princeton University Press, 2009).
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[[분류:삼각함수]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q2533727 Q2533727]
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===Spacy 패턴 목록===
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* [{'LOWER': 'exact'}, {'LOWER': 'trigonometric'}, {'LEMMA': 'constant'}]

2021년 2월 17일 (수) 05:47 기준 최신판

개요



삼각함수 표의 역사



표만들기 기술



톨레미 '알마게스트'

인도의 삼각함수



이슬람에서의 발전



동아시아의 삼각함수



유럽의 삼각함수

  • 레티쿠스
  • 피티스쿠스



푸리에

  • 1807


연표



메모

Ptolemy was well aware of the new possibilities, because finding the distance between two stars was equivalent to measuring an arc of a circle, and he adapted the spherical geometry for use with tables of chords. http://nrich.maths.org/6853&part=

Of course, many of the astronomical calculations Ptolemy needed to perform concerned the angular distances between celestial bodies or, in other words, the positions of bodies on a spherical surface, for which spherical trigonometry is appropriate. Here, too, Ptolemy could use his table of chords.

While many new aspects of trigonometry were being discovered, the chord, sine, versine and cosine were developed in the investigation of astronomical problems, and conceived of as properties of angles at the centre of the heavenly sphere. In contrast, tangent and cotangent properties were derived from the measurement of shadows of a gnomon and the problems of telling the time. http://nrich.maths.org/6908&part=



The sine formula for spherical triangleswas used to good effect by the famous Islamic scholar al-B¯ır¯un¯ı with his solution to the qibla problem, this being to determine the direction in which Mecca was closest from a given location on the Earth, i.e. along a great circle



시간과 주기운동 http://en.wikipedia.org/wiki/Atomic_clock

http://en.wikipedia.org/wiki/Spring_%28device%29

시계종류 : sundial, water, divisional time, pendulum, quartz, atomic clock http://www.youtube.com/watch?v=4T8uyD0AvzI



관련된 항목들



수학용어번역



사전 형태의 자료


관련논문



관련도서

  • Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (Princeton University Press, 2009).

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'exact'}, {'LOWER': 'trigonometric'}, {'LEMMA': 'constant'}]