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Matematik Teoremlerinin Antik Dönem Mozaikleri Üzerinde Tespiti

Year 2023, Issue: 16, 39 - 61, 03.11.2023
https://doi.org/10.26658/jmr.1376705

Abstract

Bu çalışmanın amacı, Antik Dönem’de matematik bilgisinin mozaik sanatına yansımasının incelenmesi ve değerlendirilmesidir. Matematik tarihi ve mozaik sanatının karşılaştırılması sonucu, en bilinen matematik teoremleri ve mozaik motifleri arasında formların doğası üzerinden bir bağlantı kurulmuştur. Örneğin svastika, meander, spiral, küp ve prizma formları ve Khioslu Hippokrates’in lunar alanlar hesabı ile ilgili grafikten üretilebilen formlar analiz edilmiştir. Ayrıca, İskenderiyeli Pappus’un altıgenleri ve Arkhimedes’in yarı düzgün katıları ile benzerlik gösteren formların tespitine yönelik analizler, tartışmalar ve değerlendirmeler sunulmuştur. Bu çalışmada kullanılan yöntemlerin ve elde edilen bilgilerin; mozaik sanatı ve matematik tarihi araştırmalarına, arkeolojik eserlerin belgelenmesine ve değerlendirilmesine, müzecilik uygulamalarına ve konservasyon çalışmalarına katkı sağlayacağı düşünülmektedir.

References

  • Aydoğdu 2022 E. Aydoğdu, The Reflection of Mathematic Knowledge on the Arts of Mosaic and Sculpture, Unpublished PhD Thesis, Dokuz Eylül University, İzmir.
  • Balmelle – Darmon 1986 C. Balmelle – J.-P. Darmon, “L’artisan-mosaïste dans l’Antiquité tardive. Réflexion à partir des signatures”, Colloque international, Artistes, artisans et production artistique au Moyen-Age, Rennes, Centre national de la recherche scientifique, Université de Rennes II, Haute-Bretagne, vol. I: Les hommes, Paris, 235-253.
  • Barbaro 1568 D. Barbaro, La pratica della perspettiva, Venice.
  • Blake 1930 M. E. Blake, “The Pavements of the Roman Buildings of the Republic and Early Empire”, MemAmAc 8, 7-159.
  • Boyer 1968 C. B. Boyer, A History of Mathematics, USA.
  • Bruneau 1987 P. Bruneau, La mosaïque antique, [Lectures en Sorbonne], Paris.
  • Cajori 1918 F. Cajori, “Pierre Laurent Wantzel”, Bulletin of the American Mathematical Society 24/7, 339-347.
  • Daszewski – Michaelides 1989 W. A. Daszewski – D. Michaelides, Guide des mosaïques de Paphos, Nicosia.
  • Décor I C. Balmelle – M. Blanchard Lemée – J. Christophe – J.-P. Darmon – A.-M. Guimier Sorbets – H. Lavagne – R. Prudhomme – H. Stern, Le Décor géométrique de la mosaïque romaine I, Paris, 1985.
  • Décor II C. Balmelle – M. Blanchard-Lemée – J.- P. Darmon – S. Gozlan – M. P. Raynaud, Le Décor géométrique de la mosaïque romaine II, Paris, 2002.
  • De Vos 1991 M. De Vos, “Paving Techniques at Pompeii”, ANews 16, 36-60.
  • Dunbabin 1999 K. M. D. Dunbabin, Mosaics of the Greek and Roman World, Cambridge.
  • Duran-Kremer 2012 M. de J. Duran-Kremer, “Floral and Geometrical Motives of the Pavement Mosaics in East and West. The Example of the Roman Villa of Abicada”, JMR 5, 59-70.
  • Dürer 1525 A. Dürer, Vnderweysung der Messung/mit dem Zirckel vn[d] Richtscheyt/in Linien Ebnen und gantzen Corporen/durch Albrecht Dü rer zusammen getzoge[n]/vnd zu Nutz alle[n] Kunstlieb habenden mit zuugehörigen Figuren/in Truck gebracht/im Jahr M.D.XXv., Nuremberg.
  • Eukl. elem. Euclid, The Thirteen Books of Euclid’s Elements, Vol III (Book X-XIII), Translated by Thomas Little Heath, Cambridge, 1968.
  • Heath 1897 T. L. Heath, The Works of Archimedes, Cambridge.
  • Heath 1921a T. Heath, A History of Greek Mathematics, Vol. I: From Thales to Euclid, Oxford.
  • Heath 1921b T. Heath, A History of Greek Mathematics, Volume II, From Aristarchus to Diophantus, Oxford.
  • Kepleri 1864 J. Kepleri, Astronomi, Opera Omnia, Vol. 5, Ch. Frisch (ed.), Francofurti A. M. et Erlangae, Heyder & Zimmer.
  • Keppleri 1619 I. Keppleri, Harmonices Mundi, Libri V Quorum, sumptibus Godofredi Tampachii Bibl. Francof. Excudebat Ioannes Plancus, Linz.
  • Lassus 1971 J. Lassus, “Remarques sur les mosaïques de Vaison-la-Romaine”, Gallia 29-1, 45-72.
  • López Monteagudo – Neira 2010 G. López Monteagudo – L. Neira, “Mosaico”, P. León (coord.), Arte Romano de la Bética III, Mosaico, Pintura, Manufacturas, Sevilla, 17-189.
  • Pacioli 1509 L. Pacioli, Divina proportione opera a tutti glingegni perspicaci e curiosi necessaria oue ciascun studioso di philosophia: prospectiua pictura sculptura: architectura: musica: e altre mathematice: suavissima: sottile: e admirabile doctrina consequira: e delectarassi: co [n] varie questione de secretissima scientia, A. Paganius Paganinus characteribus elegantissimis accuratissime imprimebat, Venice.
  • Pappus. Synagoge Pappus, Pappi Alexandrini Colectionis, Volumen III, Tomus I: Insunt Libri VIII Reliquiae, Suplementa In Pappi Collectionem, Friedricus Hultsch (ed.), Berlin, 1878.
  • Penedo 1993 M. D. Penedo, Iconografía de los mosaicos romanos en la Hispania alto-imperial, Univesitat Rovira i Virgili, Barcelona.
  • Plat. Tim. J. M. Cooper – D. S. Hutchinson (eds.), Plato: Complete Works, Hackett Publishing Company, Cambridge, 1997.
  • Procl. On Euclid I Proclus, A Commentary on the First Book of Euclid’s Elements, Translated by Galen Raymond Morrow, Princeton Univcersity Press, Princeton, New Jersey, 1970.
  • Tavares – Freitas 2018 H. Tavares – P. J. Freitas, “Dividing the Circle”, The College Mathematics Journal 49/3, 187-194.
  • Taylor 1942 R. E. Taylor, No Royal Road: Luca Pacioli and His Times, North Carolina.
  • Thompson 1925 D. W. Thompson, “On the Thirteen Semi-Regular Solids of Archimedes, and on Their Development by the Transformation of Certain Plane Configurations”, Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character 107/742, 181-188.
  • Vargas Vázquez 2017 S. Vargas Vázquez, “Geometric Mosaics of Baetica”, JMR 10, 347-364.
  • Vitr. Vitruvius, Ten Books on Architecture, M. H. Morgan (trans.), London, 1914.
  • Wantzel 1837 P.-L. Wantzel, “Recherches sur les moyens de reconnaître si un problème de géométrie peut se résoudre avec la règle et le compas”, Journal de Mathématiques Pures et Appliquées 1/2, 366-372.

Determination of the Mathematical Theorems on Ancient Mosaics

Year 2023, Issue: 16, 39 - 61, 03.11.2023
https://doi.org/10.26658/jmr.1376705

Abstract

The aim of this research is to examine and evaluate the reflection of mathematical knowledge on examples of ancient mosaic art. As a result of the comparison between history of mathematics and art of mosaics, a connection has been made between the well-known theorems and patterns through the nature of the forms. For this purpose, patterns like swastika, meander, spiral and cube forms, as well as the forms that can be produced from the graph related to the lunar area calculation of Hippocrates of Chios have been analyzed. In addition, analyzes, discussions and evaluations on the identification of the forms similar to the semi-regular solids of Archimedes and the hexagons of Pappus of Alexandria have been presented. It is thought that the methods used and the information obtained in this study will contribute to the research of mosaic art and history of mathematics, the documentation and evaluation of archaeological artifacts, the museology practices and conservation studies.

References

  • Aydoğdu 2022 E. Aydoğdu, The Reflection of Mathematic Knowledge on the Arts of Mosaic and Sculpture, Unpublished PhD Thesis, Dokuz Eylül University, İzmir.
  • Balmelle – Darmon 1986 C. Balmelle – J.-P. Darmon, “L’artisan-mosaïste dans l’Antiquité tardive. Réflexion à partir des signatures”, Colloque international, Artistes, artisans et production artistique au Moyen-Age, Rennes, Centre national de la recherche scientifique, Université de Rennes II, Haute-Bretagne, vol. I: Les hommes, Paris, 235-253.
  • Barbaro 1568 D. Barbaro, La pratica della perspettiva, Venice.
  • Blake 1930 M. E. Blake, “The Pavements of the Roman Buildings of the Republic and Early Empire”, MemAmAc 8, 7-159.
  • Boyer 1968 C. B. Boyer, A History of Mathematics, USA.
  • Bruneau 1987 P. Bruneau, La mosaïque antique, [Lectures en Sorbonne], Paris.
  • Cajori 1918 F. Cajori, “Pierre Laurent Wantzel”, Bulletin of the American Mathematical Society 24/7, 339-347.
  • Daszewski – Michaelides 1989 W. A. Daszewski – D. Michaelides, Guide des mosaïques de Paphos, Nicosia.
  • Décor I C. Balmelle – M. Blanchard Lemée – J. Christophe – J.-P. Darmon – A.-M. Guimier Sorbets – H. Lavagne – R. Prudhomme – H. Stern, Le Décor géométrique de la mosaïque romaine I, Paris, 1985.
  • Décor II C. Balmelle – M. Blanchard-Lemée – J.- P. Darmon – S. Gozlan – M. P. Raynaud, Le Décor géométrique de la mosaïque romaine II, Paris, 2002.
  • De Vos 1991 M. De Vos, “Paving Techniques at Pompeii”, ANews 16, 36-60.
  • Dunbabin 1999 K. M. D. Dunbabin, Mosaics of the Greek and Roman World, Cambridge.
  • Duran-Kremer 2012 M. de J. Duran-Kremer, “Floral and Geometrical Motives of the Pavement Mosaics in East and West. The Example of the Roman Villa of Abicada”, JMR 5, 59-70.
  • Dürer 1525 A. Dürer, Vnderweysung der Messung/mit dem Zirckel vn[d] Richtscheyt/in Linien Ebnen und gantzen Corporen/durch Albrecht Dü rer zusammen getzoge[n]/vnd zu Nutz alle[n] Kunstlieb habenden mit zuugehörigen Figuren/in Truck gebracht/im Jahr M.D.XXv., Nuremberg.
  • Eukl. elem. Euclid, The Thirteen Books of Euclid’s Elements, Vol III (Book X-XIII), Translated by Thomas Little Heath, Cambridge, 1968.
  • Heath 1897 T. L. Heath, The Works of Archimedes, Cambridge.
  • Heath 1921a T. Heath, A History of Greek Mathematics, Vol. I: From Thales to Euclid, Oxford.
  • Heath 1921b T. Heath, A History of Greek Mathematics, Volume II, From Aristarchus to Diophantus, Oxford.
  • Kepleri 1864 J. Kepleri, Astronomi, Opera Omnia, Vol. 5, Ch. Frisch (ed.), Francofurti A. M. et Erlangae, Heyder & Zimmer.
  • Keppleri 1619 I. Keppleri, Harmonices Mundi, Libri V Quorum, sumptibus Godofredi Tampachii Bibl. Francof. Excudebat Ioannes Plancus, Linz.
  • Lassus 1971 J. Lassus, “Remarques sur les mosaïques de Vaison-la-Romaine”, Gallia 29-1, 45-72.
  • López Monteagudo – Neira 2010 G. López Monteagudo – L. Neira, “Mosaico”, P. León (coord.), Arte Romano de la Bética III, Mosaico, Pintura, Manufacturas, Sevilla, 17-189.
  • Pacioli 1509 L. Pacioli, Divina proportione opera a tutti glingegni perspicaci e curiosi necessaria oue ciascun studioso di philosophia: prospectiua pictura sculptura: architectura: musica: e altre mathematice: suavissima: sottile: e admirabile doctrina consequira: e delectarassi: co [n] varie questione de secretissima scientia, A. Paganius Paganinus characteribus elegantissimis accuratissime imprimebat, Venice.
  • Pappus. Synagoge Pappus, Pappi Alexandrini Colectionis, Volumen III, Tomus I: Insunt Libri VIII Reliquiae, Suplementa In Pappi Collectionem, Friedricus Hultsch (ed.), Berlin, 1878.
  • Penedo 1993 M. D. Penedo, Iconografía de los mosaicos romanos en la Hispania alto-imperial, Univesitat Rovira i Virgili, Barcelona.
  • Plat. Tim. J. M. Cooper – D. S. Hutchinson (eds.), Plato: Complete Works, Hackett Publishing Company, Cambridge, 1997.
  • Procl. On Euclid I Proclus, A Commentary on the First Book of Euclid’s Elements, Translated by Galen Raymond Morrow, Princeton Univcersity Press, Princeton, New Jersey, 1970.
  • Tavares – Freitas 2018 H. Tavares – P. J. Freitas, “Dividing the Circle”, The College Mathematics Journal 49/3, 187-194.
  • Taylor 1942 R. E. Taylor, No Royal Road: Luca Pacioli and His Times, North Carolina.
  • Thompson 1925 D. W. Thompson, “On the Thirteen Semi-Regular Solids of Archimedes, and on Their Development by the Transformation of Certain Plane Configurations”, Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character 107/742, 181-188.
  • Vargas Vázquez 2017 S. Vargas Vázquez, “Geometric Mosaics of Baetica”, JMR 10, 347-364.
  • Vitr. Vitruvius, Ten Books on Architecture, M. H. Morgan (trans.), London, 1914.
  • Wantzel 1837 P.-L. Wantzel, “Recherches sur les moyens de reconnaître si un problème de géométrie peut se résoudre avec la règle et le compas”, Journal de Mathématiques Pures et Appliquées 1/2, 366-372.
There are 33 citations in total.

Details

Primary Language English
Subjects Archaeological Science
Journal Section Article
Authors

Erhan Aydoğdu

Ali Kazım Öz

Publication Date November 3, 2023
Published in Issue Year 2023 Issue: 16

Cite

APA Aydoğdu, E., & Öz, A. K. (2023). Determination of the Mathematical Theorems on Ancient Mosaics. Journal of Mosaic Research(16), 39-61. https://doi.org/10.26658/jmr.1376705
AMA Aydoğdu E, Öz AK. Determination of the Mathematical Theorems on Ancient Mosaics. JMR. November 2023;(16):39-61. doi:10.26658/jmr.1376705
Chicago Aydoğdu, Erhan, and Ali Kazım Öz. “Determination of the Mathematical Theorems on Ancient Mosaics”. Journal of Mosaic Research, no. 16 (November 2023): 39-61. https://doi.org/10.26658/jmr.1376705.
EndNote Aydoğdu E, Öz AK (November 1, 2023) Determination of the Mathematical Theorems on Ancient Mosaics. Journal of Mosaic Research 16 39–61.
IEEE E. Aydoğdu and A. K. Öz, “Determination of the Mathematical Theorems on Ancient Mosaics”, JMR, no. 16, pp. 39–61, November 2023, doi: 10.26658/jmr.1376705.
ISNAD Aydoğdu, Erhan - Öz, Ali Kazım. “Determination of the Mathematical Theorems on Ancient Mosaics”. Journal of Mosaic Research 16 (November 2023), 39-61. https://doi.org/10.26658/jmr.1376705.
JAMA Aydoğdu E, Öz AK. Determination of the Mathematical Theorems on Ancient Mosaics. JMR. 2023;:39–61.
MLA Aydoğdu, Erhan and Ali Kazım Öz. “Determination of the Mathematical Theorems on Ancient Mosaics”. Journal of Mosaic Research, no. 16, 2023, pp. 39-61, doi:10.26658/jmr.1376705.
Vancouver Aydoğdu E, Öz AK. Determination of the Mathematical Theorems on Ancient Mosaics. JMR. 2023(16):39-61.

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