Zen master12/5/2023 We prefer to formulate and solve problems with elementary tools, even though some of them can also be read with the language of Euclidean Geometry, Combinatorics and Graph Theory. We do not know whether such formulation already exists in literature. In this paper, taking inspiration from the Kyoto garden, we suggest didactics kōan that may help to appreciate the importance of the symmetry in these constructions. This is an a-posteriori approach focused on the visual perception, whereas we imagine the garden in the moment of its construction. In particular, the authors show local axes of symmetry among the rocks by using medial axis transformations. On the other hand, the presence and breaking of symmetry of the Ryōan-ji garden has been analyzed in Van Tonder et al. A good reference for this subject is Fukagawa and Rothman ( 2008) unfortunately, the Ryōan-ji is not present in this book. Japanese gardens and temples have already inspired mathematical problems, originally written on wooden blocks. The points will correspond to the rocks in a kare-sansui garden. With a mathematical eye, we simplify the setting and present several problems about points arrangements in a rectangle. While listening to this story, we imagine the dialogue between a Master and a Monk for realizing this garden. Deeper meditation is necessary to construct this special arrangement of stones so that not all of them can be seen at once. Someone says that the Ryōan-ji garden is a kōan, a riddle that helps in meditation. The kare-sansui garden in the Zen Buddhist temples is a dry garden made of stones, smooth pebbles and moss.
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