Mathematical Determination of the Cultural Interaction between Medieval Groups

Yıl 2020, , 95 - 101, 31.08.2020

Mehmet Erbudak

https://doi.org/10.33187/jmsm.680161

Cited By: 4

Öz

A mathematical classification of two-dimensional ornaments into 17 plane symmetry groups is presented, which were created by five medieval cultural groups of Middle East. The data are considered representative for the cultural groups. By applying a correlation algorithm on the individual use of symmetry classes by each cultural group, the strength of the interaction between the pairs of groups are quantitatively determined. The analysis shows that the strongest similarity in the creation of periodic ornaments is between Rum Seljuks and Arab Muslims. It is also found that the Rum Seljuks, followed by Armenians, are the most interactive cultures. This report is the first attempt to quantify cultural communication by mathematical means.

Anahtar Kelimeler

Correlation, Medieval architecture, Ornaments

Kaynakça

• [1] C. Brinton, J. B. Christopher, R. L. Wolff, A History of Civilization Vol. I, Prentice Hall, Englewood, NJ, 1960.
• [2] D. K. Washburn, D. W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press, Washington DC, 1991.
• [3] D. Schattschneider, The plane symmetry groups: Their recognition and notation, Amer. Math. Monthly, 85(6) (1978), 439-450.
• [4] L. Jones, Between Islam and Byzantium, Ashgate, Burlington, VT, 2007.
• [5] J. J. Norwich, Byzantium, The Early Centuries, The Apogee, The Decline and Fall, Alfred A. Knopf, NY, 1997.
• [6] A. E. Kaldellis, Romanland: Ethnicity and Empire in Byzantium, Harvard University Press, Cambridge, MA, 2019.
• [7] M. Hattstein, P. Delius, Islam, Kunst und Architektur, K¨onemann, K¨oln, 2000.
• [8] S. R. Canby, D. Beyazit, M. Rugiadi, A. C. S. Peacock, Court and Cosmos, The Great Age of the Seljuqs, The Metropolitan Museum of Art, NY, 2016.
• [9] A. Hutt, L. Harrow, Iran 1, Scorpion Publications, London, 1977.
• [10] A. Bas¸an, The Great Seljuks: A History, Routledge, London, 2010.
• [11] S. Mecit, The Rum Seljuqs: Evolution of a Dynasty, Routledge, London, 2014.
• [12] G. Schneider, Geometrische Bauornamente der Seldschuken in Kleinasien, Dr. Ludwig Reichert, Wiesbaden, 1980.
• [13] C. Hammond, The Basics of Crystallography and Diffraction, 4. Ed., Oxford Univ. Press, Oxford, 2015.
• [14] G. Polya, Über die analogie der kristallsymmetrie in der ebene, Z. Kristall., 60 (1924), 278-282.
• [15] E. A. Müller, Gruppentheoretische und strukturanalytische Untersuchung der Maurischen Ornamente aus der Alhambra in Granada, Ph.D. Thesis, University of Zurich, 1944; El estudio ornamentos como applicati´on de la teor´ıa de los grupos de orden finito, Euclides (Madrid), 6 (1946), 42-52.
• [16] M. Erbudak, Symmetry analysis of the floor ornaments of the San Marco Cathedral in Venice, Heliyon, 5 (2019), e01320.
• [17] M. Erbudak, A. Kyurkchyan, Armenian, Byzantine and Islamic Ornaments, Influences Among Neighbors, Kyurkchyan, Yerevan, 2019, doi.org/10.3929/ethz-b-000394011.
• [18] A. Kyurkchyan (Author), H. H. Khatcherian (Photographer), Armenian Ornamental Art, Craftology, Yerevan, 2010.
• [19] J. Bourgoin, Les E`le`ments de L’Arabe, Librairie de Firmin-Didot, Paris, 1879; Arabic Geometrical Pattern and Design, Dover, New York, 1973.
• [20] E. Makovicky, M. Malovicky, Arabic Geometrical Patterns – A Treasury for Crystallographic Teaching, Neues Jahrbuch f¨ur Mineralogie Monatshefte, 2 (1977), 58-68; S. J. Abas, A. S. Salman, Symmetries of Islamic Geometrical Patterns, World Scientific, Singapore, 1995.
• [21] E. Makovicky, Symmetry, De Gruyter, Berlin, 2016.
• [22] J. Bonner, Islamic Geometric Patterns, Springer, New York, 2017.
• [23] Available at https://en.wikipedia.org:Pearson_correlation_coefficient.
• [24] J. Ye, Cosine similarity measures for intuitionistic fuzzy sets and their applications, Math. Comput. Modelling, 53 (2011), 91-97.
• [25] K. Rudenberg, K. O-Ohata, D. G. Wilson, Overlap integrals between atomic orbitals, J. Math. Phys., 7 (3) (1966), 539-546.