# 방원도의 투영

• Accepted : 2014.12.18
• Published : 2014.12.31
• 91 45

#### Abstract

When the circle inscribed in a square is projected to a picture plane, one sees, in general, an ellipse in a convex quadrilateral. This ellipse is poorly described in the works of Alberti and Durer. There are one parameter family of ellipses inscribed in a convex quadrilateral. Among them only one ellipse is the perspective image of the circle inscribed in the square. We call this ellipse "the projected ellipse." One can easily find the four tangential points of the projected ellipse and the quadrilateral. Then we show how to find the center of the projected ellipse. Finally, we describe a pair of conjugate vectors for the projected ellipse, which finishes the construction of the desired ellipse. Using this algorithm, one can draw the perspective image of the squared-circle tiling.

#### Keywords

ellipse;conic;perspective

#### References

1. L. Alberti, Della Pittura, 1435. 알베르티 지음, 노성두 옮김, 알베르티의 회화론, 사계절, 1998, 2004.
2. D. Brannan, M. Esplen, J. Gray, Geometry, Cambridge Univ. Press, 1999.
3. J. V. Field, The Invention of Infinity, Oxford Univ. Press, 1997, 2005.
4. M. Henle, Modern Geometries, Prentice Hall, 1997.
5. Jin J.-K., History of European Arts, Humanist, 2008. 진중권, 서양미술사, 고전예술편, 휴머 니스트, 2008.
6. Kim H.-J., Mathematics in Civilization, HyoHyeong, 2009. 김홍종, 문명, 수학의 필하모니, 효형, 2009.
7. A. Ostermann, G. Wanner, Geometry by Its History, Springer, 2012.
8. E. Panofsky, The Life and Art of Albrecht Durer, Princeton Univ. Press, 1943. (에르빈 파 노프스키 지음, 이산 옮김, 인문주의 예술가 뒤러, 한길아트, 2006.)