삼각함수의 역사

개요

• History of Trigonometry Part 1
• History of Trigonometry Part 2
• History of Trigonometry Part 3

 

 

삼각함수 표의 역사

• http://www.wolframalpha.com/input/?i=sin(pi/180)+in+base+60
• 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.amazon.com/Episodes-History-Mathematics-Mathematical-Library/dp/0883856131

 

 

표만들기 기술

• http://en.wikipedia.org/wiki/Exact_trigonometric_constants
• 삼각함수의 값

 

 

 

 

 

인도의 삼각함수

• http://en.wikipedia.org/wiki/Aryabhata%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:10.1006/hmat.1997.2160.

 

 

이슬람에서의 발전

• Al-Khwārizmī's Sine Tables and a Western Table with the Hindu Norm of R = 150
• 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=koei=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).
  • 지구 크기의 측정 http://www.jscimath.org/uploads/J2010145AG.pdf?CFID=1980504&CFTOKEN=51765461&jsessionid=84303618f42d5fc6af37543e5fa6358265d7

• http://en.wikipedia.org/wiki/Islamic_astronomy
• http://en.wikipedia.org/wiki/Geography_and_cartography_in_the_Caliphate

 

 

동아시아의 삼각함수

• 한국의 수학http://www.wolframalpha.com/input/?i=sin+(pi*(25%2B42/60%2B51/3600)/180)

 

 

유럽의 삼각함수

• 레기오몬타누스
  • http://www.hps.cam.ac.uk/starry/regiotables.html

• [1]http://deadscientistoftheweek.blogspot.com/2010/06/regiomontanus.html
• Götz, Ottomar, and Dirk Huylebrouck. 2003. Regiomontanus. The Mathematical Intelligencer 25, no. 3 (9): 44-46. doi:10.1007/BF02984849.

• 레티쿠스
• 피티스쿠스

 

 

푸리에

• 1807

 

연표

• 1464년 레기오몬타누스 De Triangulis Omnimodis (Concerning Triangles of Every Kind) 작업 시작, 1533년 출판됨
• 1533년 프리시우스(Gemma Frisius) 가 삼각측량법을 발견 http://en.wikipedia.org/wiki/Gemma_Frisius
• 1551년 레티쿠스 Canon doctrinae triangulorum (Canon of the Science of Triangles) 출판, 1596년 사후 제자에 의해 대작 Opus palatinum 출판
• 1595년 피티스쿠스 Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus 출판, 1607년 레티쿠스의 Opus palatinum에서 발견된 오류를 수정 http://en.wikipedia.org/wiki/Bartholomaeus_Pitiscus
• 1678년 후크의 법칙
• 1693년 라이프니츠 조화진동자의 급수해, 다음해 요한 베르누이 역시 급수해로 만족
• 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/~euler/pages/E126.html
  • 오일러(1707-1783)
• 1965년 4월 쿨리와 투키의 논문이 출판
• http://www.google.com/search?hl=en&tbs=tl:1&q=
• Earliest Known Uses of Some of the Words of Mathematics
• Earliest Uses of Various Mathematical Symbols
• 수학사 연표

 

 

메모

• http://oskicat.berkeley.edu/search~S1?/dTrigonometry+--+Tables./dtrigonometry+tables/-3%2C-1%2C0%2CB/exact&FF=dtrigonometry+tables&1%2C135%2C
• http://oskicat.berkeley.edu/search~S1?/dTrigonometry+--+Tables./dtrigonometry+tables/-3%2C-1%2C0%2CB/exact&FF=dtrigonometry+tables+early+works+to+1800&1%2C5%2C

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

• 뉴딜과 mathematical tables project

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=palatinum

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• [2]http://en.wikipedia.org/wiki/Almagest
• http://en.wikipedia.org/wiki/Hipparchus

 

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:10.1017/S0957423909990099.     
• Some History of the Calculus of the Trigonometric Functions
• A Note on the History of Trigonometric Functions
  • Jean-Pierre Merlet, 2004, 5, 195-200
• Katz, Victor J., “The curious history of trigonometry,” The UMAP Journal, 11 (1990), 339–354.
• VJ Katz, Calculus of the trigonometric functions, Hist. Math. 14(1987), 311-324
• Boyer, C., 1947. History of the derivative and integral of the sine. Mathematics Teacher 40, pp. 267–275.
• References for: The trigonometric functions

 

관련도서

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