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On the Evolute of Ionic Volute

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Abstract

A volute represents the most recognisable characteristic of the capital of the Ionic order. The geometric construction of its spiral form has occupied scholars since Renaissance times since Vitruvius’ description provided a variety of shapes that fit given constraints. Based on 16 analysed methods, the present research shows the continuity of the idea of drawing a Ionic volute as the involute of a polygonal chain within the eye. Namely, if a volute spiral is formed by several consecutive circular arcs, it can be defined as the involute of the polyline that connects the centres of corresponding arcs, whereby the polyline is the evolute of the chosen volute. In addition, by adopting suitable rectilinear discretisation of arithmetic and logarithmic spirals for an evolute form, two novel mathematically derived volute shapes are created. With a complete fit into Vitruvian constraints, such volutes indicate the great possibilities of the mathematical treatment of Ionic volutes.

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Acknowledgements

This research is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Project No. 451-03-68/2022-14/200156).

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  1. Department of Architecture, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, Novi Sad, 21101, Serbia

    Dimitriye Nikolić

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Correspondence to Dimitriye Nikolić.

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Nikolić, D. On the Evolute of Ionic Volute. Nexus Netw J 25, 107–132 (2023). https://doi.org/10.1007/s00004-022-00618-8

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