조화급수와 조화 평균에서 '조화'란?

간단한 소개

• 조화평균 에 대한 자세한 사항은 해당 항목 참조
  \(H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} \)
  
• 조화급수
  \(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots\)
  
• 조화급수의 각 항은
  
• Its name derives from the concept of overtones, or harmonics, in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the term harmonic mean likewise derives from music.
  
• 음악의 배음 overtone 개념에서 기원
• 고대 그리스에서 '산술'이란 자연수와 유리수의 성질을 연구하는 분야
  

 

음악과의 관계

• tonic
• octave 2:1
• fifth 3:2
• fourth 4:3

 

 

 

 

 

하위페이지

• 0 토픽용템플릿
  
  • 0 상위주제템플릿
    

 

 

 

 

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관련된 다른 주제들

• 오일러상수, 감마
• 교차비
• 수학사연표

 

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참고할만한 자료

• http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
• http://en.wikipedia.org/wiki/Harmonic_mean
• What's Harmonic about the Harmonic Series?
  
  • David E. Kullman
  • The College Mathematics Journal, Vol. 32, No. 3 (May, 2001), pp. 201-203
• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://viswiki.com/en/
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
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• 대한수학회 수학 학술 용어집

 

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