Determination of the Mathematical Theorems on Ancient Mosaics

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.

Keywords

• Mathematics
• geometry
• ancient mosaics
• theorem
• decorative patterns

Matematik Teoremlerinin Antik Dönem Mozaikleri Üzerinde Tespiti

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.

Keywords

• Matematik
• geometri
• mozaik
• teorem
• desen

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