Geometric and Aesthetic Concepts Based on Pentagonal Structures

Cornelie Leopold ()
Additional contact information
Cornelie Leopold: TUK Kaiserslautern, FATUK – Faculty of Architecture

Chapter 11 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 291-316 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_20

Ordering information: This item can be ordered from
http://www.springer.com/9783319570723

DOI: 10.1007/978-3-319-57072-3_20

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().