"픽의 정리(Pick's Theorem)"의 두 판 사이의 차이
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| 51번째 줄: | 51번째 줄: | ||
==에세이, 리뷰, 강의노트== | ==에세이, 리뷰, 강의노트== | ||
* [http://bomber0.byus.net/index.php/2008/04/23/612 픽의 정리(Pick’s Theorem)], 피타고라스의 창 | * [http://bomber0.byus.net/index.php/2008/04/23/612 픽의 정리(Pick’s Theorem)], 피타고라스의 창 | ||
| − | + | * Blatter, Christian. “Another Proof of Pick’s Area Theorem.” Mathematics Magazine 70, no. 3 (June 1, 1997): 200. doi:10.2307/2691260. http://www.jstor.org/stable/2691260 | |
| + | * Bruckheimer, Maxim, and Abraham Arcavi. “A Visual Approach to Some Elementary Number Theory.” The Mathematical Gazette 79, no. 486 (November 1, 1995): 471–78. doi:10.2307/3618072. http://www.jstor.org/stable/3618072 | ||
| + | * Grunbaum, Branko, and G. C. Shephard. “Pick’s Theorem.” The American Mathematical Monthly 100, no. 2 (February 1, 1993): 150–61. doi:10.2307/2323771. http://www.jstor.org/stable/2323771 | ||
| + | * Varberg, Dale E. “Pick’s Theorem Revisited.” The American Mathematical Monthly 92, no. 8 (October 1, 1985): 584–87. doi:10.2307/2323172. http://www.jstor.org/stable/2323172 | ||
| + | * Liu, Andy C. F. “Lattice Points and Pick’s Theorem.” Mathematics Magazine 52, no. 4 (September 1, 1979): 232–35. doi:10.2307/2689416. http://www.jstor.org/stable/2689416 | ||
| + | * Gaskell, R. W., M. S. Klamkin, and P. Watson. “Triangulations and Pick’s Theorem.” Mathematics Magazine 49, no. 1 (January 1, 1976): 35–37. doi:10.2307/2689882. http://www.jstor.org/stable/2689882 | ||
| 57번째 줄: | 62번째 줄: | ||
==관련논문== | ==관련논문== | ||
* Rosner, Haim Shraga. “An Algorithmic Approach to Pick’s Theorem.” arXiv:1407.0586 [math], July 2, 2014. http://arxiv.org/abs/1407.0586. | * Rosner, Haim Shraga. “An Algorithmic Approach to Pick’s Theorem.” arXiv:1407.0586 [math], July 2, 2014. http://arxiv.org/abs/1407.0586. | ||
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[[분류:조합수학]] | [[분류:조합수학]] | ||
2015년 8월 24일 (월) 21:19 판
개요
- 꼭지점이 격자위에 놓여 있는 다각형의 넓이를 구하는 공식
- 다각형의 내부에 있는 격자점의 개수를 $I$, 경계에 있는 격자점의 수를 $B$라 하면, 다각형의 넓이 $A$는 다음과 같이 주어진다
$$ A=I+B/2-1 $$
예
$I=6,B=6$
$A=6+6/2-1=8$
$I=5,B=10$
$A=5+10/2-1=9$
메모
역사
- 1899년
- 수학사 연표
관련된 항목들
사전 형태의 자료
매스매티카 파일 및 계산 리소스
- https://drive.google.com/file/d/0B8XXo8Tve1cxWEF0amNoNHlNbVE/view
- http://demonstrations.wolfram.com/PicksTheorem/
- http://demonstrations.wolfram.com/EstimatingPerimeterAndAreaOfSimplePolygons/
에세이, 리뷰, 강의노트
- 픽의 정리(Pick’s Theorem), 피타고라스의 창
- Blatter, Christian. “Another Proof of Pick’s Area Theorem.” Mathematics Magazine 70, no. 3 (June 1, 1997): 200. doi:10.2307/2691260. http://www.jstor.org/stable/2691260
- Bruckheimer, Maxim, and Abraham Arcavi. “A Visual Approach to Some Elementary Number Theory.” The Mathematical Gazette 79, no. 486 (November 1, 1995): 471–78. doi:10.2307/3618072. http://www.jstor.org/stable/3618072
- Grunbaum, Branko, and G. C. Shephard. “Pick’s Theorem.” The American Mathematical Monthly 100, no. 2 (February 1, 1993): 150–61. doi:10.2307/2323771. http://www.jstor.org/stable/2323771
- Varberg, Dale E. “Pick’s Theorem Revisited.” The American Mathematical Monthly 92, no. 8 (October 1, 1985): 584–87. doi:10.2307/2323172. http://www.jstor.org/stable/2323172
- Liu, Andy C. F. “Lattice Points and Pick’s Theorem.” Mathematics Magazine 52, no. 4 (September 1, 1979): 232–35. doi:10.2307/2689416. http://www.jstor.org/stable/2689416
- Gaskell, R. W., M. S. Klamkin, and P. Watson. “Triangulations and Pick’s Theorem.” Mathematics Magazine 49, no. 1 (January 1, 1976): 35–37. doi:10.2307/2689882. http://www.jstor.org/stable/2689882
관련논문
- Rosner, Haim Shraga. “An Algorithmic Approach to Pick’s Theorem.” arXiv:1407.0586 [math], July 2, 2014. http://arxiv.org/abs/1407.0586.