Dilative Rotation, Dilative Reflection in Mathematics, Nature, Art, and Education

Eleonóra Stettner () and György Emese ()
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Eleonóra Stettner: Szent István University Kaposvár Campus, Methodological Institute
György Emese: Xántus J. Bilingual Secondary School

A chapter in Complex Symmetries, 2021, pp 143-162 from Springer

Abstract: Abstract The article can be divided into three main parts. In the first part, the most common composite transformations in plane and space are defined and organized from a mathematical perspective. These are the compositions of central similitude and different isomorphisms: dilative rotation and dilative reflection. Then we talk about the relationship between the various spirals and the above-mentioned transformations. In the second part, we examine where we can meet composite symmetries in nature and certain works of art (highlighting the works of M. C. Escher and a couple of his followers). In the third part, building on the teaching experiences of the authors, we give a summary of composite symmetries on different levels of education, occurring usually only implicitly, and propose some more possibilities that can be used in or outside of class.

Keywords: Dilative rotation; dilative reflection; spirals; mathematics in arts; mathematics in nature; GeoGebra (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-88059-0_12

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DOI: 10.1007/978-3-030-88059-0_12

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