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Geometric and Aesthetic Concepts Based on Pentagonal Structures

  • Cornelie LeopoldEmail author
Living reference work entry

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Abstract

The relationship between geometry and art will be examined using the example of pentagonal structures. The work of contemporary Dutch artist Gerard Caris is based on those pentagonal structures. He calls his art work Pentagonism and questions how art creations and design processes can rely on strong, geometric, structural thinking. Pentagonal structures in plane as well as in space will be analyzed from a geometrical point of view and compared to corresponding art approaches. A review of geometric research on tessellations will be followed by a discussion on previous attempts to tile the Pentagrid with regular pentagons. The fundamental role of the Pentagrid and derivable Kite-Dart-Grid in Caris’ art design processes will also be explained. A step into the three-dimensional space leads to the dodecahedron and derived rhombohedra configurations for tessellations, or packings, in space. The geometric background refers to fundamental works by Plato, Euclid, Dürer, and Kepler as well as recent research results. The investigation will end with a discussion of the aesthetic categories of redundancy and innovation, their application to art evaluation and the differentiation of geometry and art. The example of Caris’ art, which concentrates on the regular pentagon and the spatial counterpart dodecahedron, points out the possibilities of aesthetic expressions on the basis of geometric structures. Art enables the exploration of those structures in a playful and self-explanatory way and often precedes scientific research.

Keywords

Geometry Tessellation Pentagon Pentagrid Kite-dart-grid Dodecahedron Packing Aesthetics Gerard Caris 

Notes

Acknowledgements

Many thanks to the artist Gerard Caris for the opportunity to visit him in his atelier, showing and explaining his work to me, and allowing me to get an inside view of his creation processes. The images of his works of art in the figures here are used with his kind permission, and they are managed and supported by VG Bild-Kunst, Bonn. I am grateful to Margriet Caris for helping me with all of my questions and requests.

Thank you to Zvi Hecker, who agreed to allow the use of his drawings and photos of Ramot Polin housing project to explain his design background.

Finally, many thanks to Vera Viana for her discussions on the relationship of recent topological interlocking research and Gerard Caris’ respective artworks, as well as for creating the drawings/renderings in Fig. 24 for this paper. Thank you also to Jasmine Segarra for proofreading this chapter.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.FATUK – Faculty of ArchitectureTUK KaiserslauternKaiserslauternGermany

Section editors and affiliations

  • Bharath Sriraman
    • 1
  • Kyeong-Hwa Lee
    • 2
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
  2. 2.Department of Mathematics Education, College of EducationSeoul National UniversitySeoulSouth Korea

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