"5차방정식과 정이십면체"의 두 판 사이의 차이

수학노트
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* [[뫼비우스 변환군과 기하학]]
 
* [[뫼비우스 변환군과 기하학]]
 
* [[구면기하학]]
 
* [[구면기하학]]
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2009년 12월 16일 (수) 18:48 판

이 항목의 스프링노트 원문주소

 

 

개요

 

 

invariants of the icosahedral group
  • Stereographic projections
  • vertex points
    • \(F_1=z_1z_2(z_1^{10}+11z_1^5z_2^5-z_2^{10})\)
  • face points
    • \(F_2=-(z_1^{20}+z_2^{20})+228(z_1^{15}z_2^{5}-z_1^{5}z_2^{15})-494z_1^{10}z_2^{10}\)
  • edge points
    • \(F_3=(z_1^{30}+z_2^{30})+522(z_1^{25}z_2^{5}-z_1^{5}z_2^{25})-10005(z_1^{20}z_2^{10}+z_1^{10}z_2^{20})\)

 

 

syzygy relation
  • \(1728F_1^5-F_2^3-F_3^2=0\)
  •  

 

 

역사
  • 20세기 수학의 궤도를 제시한 힐버트의 1900년 국제수학자대회 연설의 초반부 언급
  • (Mathematical Problems, Lecture delivered before the International Congress of Mathematicians at Paris in 1900 By Professor David Hilbert)

 

But it often happens also that the same special problem finds application in the most unlike branches of mathematical knowledge. So, for example, the problem of the shortest line plays a chief and historically important part in the foundations of geometry, in the theory of curved lines and surfaces, in mechanics and in the calculus of variations. And how convincingly has F. Klein, in his work on the icosahedron, pictured the significance which attaches to the problem of the regular polyhedra in elementary geometry, in group theory, in the theory of equations and in that of linear differential equations.

 

[/pages/2026224/attachments/2671447 icos1.jpg][/pages/2026224/attachments/2671449 icos2.jpg]

 

 

관련링크와 웹페이지

 

 

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