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The Japanese Theorem for Nonconvex Polygons - The Bibliography

Author(s): 
David Richeson

Acknowledgments

I would like to thank Jim Wiseman for his helpful comments during our conversations about this article. I would also like to thank the referees for their careful reading of the manuscript and many helpful suggestions. Most of all I would like to thank Ryōkwan Maruyama for the wonderfully beautiful and deep mathematical problem that he posted in the Tsuruoka-Sannōsha shrine more than two centuries ago.

Bibliography

 

[AUM1] Mangho Ahuja, Wataru Uegaki, and Kayo Matsushita. Japanese theorem: a little known theorem with many proofs—part I. Missouri J. Math. Sci., 16 (2): 72–80, 2004.

[AUM2] Mangho Ahuja, Wataru Uegaki, and Kayo Matsushita. Japanese theorem: a little known theorem with many proofs—part II. Missouri J. Math. Sci., 16 (3): 149–158, 2004.

[AUM3] Mangho Ahuja, Wataru Uegaki, and Kayo Matsushita. In search of 'the Japanese theorem.' Missouri J. Math. Sci., 18 (2): 1–8, 2006.

[AN] Claudi Alsina and Roger B. Nelson. Proof without words: Carnot's theorem for acute triangles. The College Mathematics Journal, 39 (2): 111, March 2008.

[Fu] Kagen Fujita. Zoku-Sinpeki-Sanpō, volume 2. 1807.

[FP] H. Fukagawa and D. Pedoe. Japanese temple geometry problems: san gaku. The Charles Babbage Research Centre, Winnipeg, Canada, 1989.

[FR] Hidetoshi Fukagawa and Tony Rothman. Sacred mathematics: Japanese temple geometry. Princeton University Press, Princeton, NJ, 2008.

[Gr] W. J. Greenstreet. Japanese mathematics. The Mathematical Gazette, 3 (55): 268–270, January 1906.

[Haw] Cathy Hawn. A Study of the Japanese Theorem. Masters degree thesis, Southeast Missouri State University, May 1996.

[Hay] T. Hayashi. Sur un soi-disant théorème Chinois. Mathesis, III (6): 257–260, 1906.

[Ho] Ross Honsberger. Mathematical gems III, volume 9 of The Dolciani Mathematical Expositions. Mathematical Association of America, Washington, DC, 1985.

[Jo1] Roger A. Johnson. Modern geometry: An elementary treatise on the geometry of the triangle and the circle. The Riverside Press, Cambridge, MA, 1929.

[Jo2] Roger A. Johnson. Advanced Euclidean geometry: An elementary treatise on the geometry of the triangle and the circle. Dover Publications Inc., New York, 1960.

[L] Timothy Lambert. The Delaunay triangulation maximizes the mean inradius. Proc. of the 6th Canadian Conf. on Computational Geometry (CCCG '94), 201–206, 1994.

[Ma] Nick Mackinnon. Friends in youth: Aspects of the use of computers in mathematics education. The Mathematical Gazette, 77 (478): 2–25, March 1993.

[Mi] Y. Mikami. A Chinese theorem in geometry. Archiv der Mathematik und Physik,3 (9): 308–310, 1905.

[R] Clark Robinson. Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. CRC Press, Boca Raton, 1995.

[Yo] T. Yosida. Zoku Sinpeki Sanpō Kai, volume 2. date unknown.

David Richeson, "The Japanese Theorem for Nonconvex Polygons - The Bibliography," Loci (December 2013)

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