원근법과 수학

이 항목의 스프링노트 원문주소

• 원근법과 수학

 

 

개요

• 사영기하학
• 선형원근법(linear perspective)
• 지평선 (horizon) 
  
  • 사영평면에서는 line at infinity 라 한다
• 눈높이 (eye-level)
• 소실점 (vanishing point)
  
  • 사영평면에서는 point at infinity라 한다

 

 

마스카니 테라스(Terrazza Mascagni)

• 토스카나 리보르노
• 평행선들은 소실점 (vanishing point)에서 만나며, 소실점이 지평선에 놓여 있음을 확인할 수 있다
• http://www.livornotop.com/servizi/foto/foto%20angelica/Livorno%20foto%20di%20Angelica.htm
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• http://livornodailyphoto.blogspot.com/2009/11/tiles.html

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1점 원근법

• 1점 원근법

 

 

2점 원근법

• 2 Point Perspective Tutorial - Mechanical Drawing Perspective Grid
• 2점 원근법

 

 

3점 원근법

• 3점 원근법

 

 

역사

• http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html
• http://www.tfaoi.com/aa/3aa/3aa127.htm
• 지오토(1267 - 1337)
• 브루넬레스키(1377 - 1446)
• 도나텔로
  
  • 원근법이 활용된 조각 Feast of Herod
• 마사치오(1401 - 1428)
  
  • 원근법이 활용된 첫번째 회화작품 http://en.wikipedia.org/wiki/Holy_Trinity_(Masaccio)
• 알베르티(1404 -1472)
  
  • 투시원근법에 대한 첫 교과서 출판 Della pittura (1435)
  •  
• 피에로 델라 프란체스카(1415- 1492)
  
  • 1474년 De Prospectiva Pingendi (On the perspective of painting) 출판
  • Flagellation of Christ (Piero della Francesca)
• 알브레히트 뒤러(1471 - 1528)
  
  • http://virtualterritory.wordpress.com/2008/10/02/a-page-out-of-durers-own-copy-of-the-painters-manual/
  • [1]http://architecturalphotogrammetry.wordpress.com/2010/03/03/understanding-photogrammetry-thanks-to-albrecht-durer/
  • http://commons.wikimedia.org/wiki/File:D%C3%BCrer_-_Zeichner_und_Akt.jpg
  • http://virtualterritory.wordpress.com/2008/10/05/one-of-duerers-prints-in-the-context-of-gender-feminism-and-other-theories/
• 데자르그(1591–1661)
• 파스칼(1623 –1662)
• 베르미어(1632-1675)
  
  • 카메라 옵스큐라의 사용
  • http://www.flickr.com/photos/arisan/4002462708/
• 퐁슬레(1788-1867)
• http://www.google.com/search?hl=en&tbs=tl:1&q=linear+perspective
• http://www.google.com/search?hl=en&tbs=tl:1&q=projective+geometry+perspective+drawing
• http://www.google.com/search?hl=en&tbs=tl:1&q=costruzione+legittima
• 수학사연표
•  

 

 

 

메모

• 소실점의 종류 http://labica.springnote.com/pages/5317735
• Basic Principles Of Perspective Drawing For The Technical Illustrator
  
  • Kevin Hulsey
• A Note on the Mathematics of Two- and Three- Point Perspective
  
  • Brian A. Barsky
• 도구
  
  • http://sketchup.google.com/
  • http://www.sketchupartists.org/tutorials/perspective-drawing-from-sketchup/
  • http://jimleggitt.typepad.com/jim-leggitt-drawing-shortcuts/2010/02/creating-perspectives-with-sketchup.html 
    

 

 

관련된 항목들

• 수학과 미술
• 타원과 인간
• 지도와 수학

 

 

수학용어번역

• point at infinity 무한원점
• http://www.google.com/dictionary?langpair=en|ko&q=무한원점
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=infinity
• 대한수학회 수학용어한글화 게시판

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/원근법
• 소실점 (두산백과)
• http://newdle.edupia.com/xmlView.aspx?xmldid=22116#p2
• http://en.wikipedia.org/wiki/Perspective_(graphical)
• http://en.wikipedia.org/wiki/Vanishing_point
• http://en.wikipedia.org/wiki/Worm%27s-eye_view
• http://en.wikipedia.org/wiki/
• http://www.wolframalpha.com/input/?i=
• NIST Digital Library of Mathematical Functions
• The On-Line Encyclopedia of Integer Sequences
  
  • http://www.research.att.com/~njas/sequences/?q=

 

 

관련논문

• Speculations on the Origins of Linear Perspective
  Including analyses of Masaccio’s Trinity and Piero’s Flagellation
  Richard Talbot
• Alberti's Perspective: A Mathematical Comment
  
  • Judy Green and Paul S. Green, The Art Bulletin, Vol. 69, No. 4 (Dec., 1987), pp. 641-645
• Ptolemy and the Origins of Linear Perspective
  
  • Kim H. Veltman, 1980
• L. B. ALBERTI'S ‘COSTRUZIONE LEGITTIMA’
  
  • Grayson, C., Italian Studies, Volume 19, 1964 , pp. 14-27(14)
• The Perspective of Piero della Francesca's 'Flagellation'
  
  • R. Wittkower and B. A. R. Carter, Journal of the Warburg and Courtauld Institutes Vol. 16, No. 3/4 (1953), pp. 292-302
• http://www.jstororg/action/doBasicSearch?Query=perspective+drawing+projective
• http://www.jstor.org/action/doBasicSearch?Query=
• http://dx.doi.org/

 

 

관련도서

• Perspective Drawing Handbook
• Piero Della Francesca: a mathematician's art
• The Geometry of an Art The History of the Mathematical Theory of Perspective from Alberti to Monge
  
  • Kirsti Andersen
• Foundations of Projective Geometry
  
  • Robin Hartshorne
• The Renaissance rediscovery of linear perspective
  
  • Edgerton, Samuel Y. Basic Books, c1975.
• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=
• 도서검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/mainSearch.do?query=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

 

관련링크와 웹페이지

• The Geometry of Perspective Drawing on the Computer
  
• The History and Theory of Perspective
  

• Alberti's Perspective Construction
  
  • AMS Feature Column

 

 

 

관련기사

• [김영나의 서양미술산책 [21] 원근법]
  
  • 김영나, 원근법, 2009-9-22
• [생활속의 수학 원근법 이론무장은 `사영기하학` 덕]
  
  • 박경미, 중앙일보, 2003-8-20
• 네이버 뉴스 검색 (키워드 수정)
  
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=수학원근법
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=소실점
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=미술사영기하학
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=알베르티원근법
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

 

블로그

• 뇌는 대수기하를 몰라도 눈은 대수기하를 안다 – 원근법
• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=원근법사영기하학
• 네이버 오늘의과학
• 수학동아
• Mathematical Moments from the AMS
• BetterExplained