Lobke, and Other Constructions from Conical Segments

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Tom Verhoeff and Koos Verhoeff: Lobke, and Other Constructions from Conical Segments. In: Bridges 2014. Pages 309–316



Lobke is a mathematical sculpture designed and constructed by Koos Verhoeff, using conical segments. We analyze its construction and describe a generalization, similar in overall structure but with a varying number of lobes. Next, we investigate a further generalization, where conical segments are connected in different ways to construct a closed strip. We extend 3D turtle geometry with a command to generate strips of connected conical segments, and present a number of interesting shapes based on congruent conical segments. Finally, we show how this relates to the skew miter joints and regular constant-torsion 3D polygons that we studied earlier.

Extended Abstract


Used References

[1] J. Barrallo, S. S ́anchez-Beitia, F. Gonz ́alez-Quintial. “Geometry Experiments with Richard Serra’s Sculpture”, Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, pp.287–294.

[2] C.H. S ́equin, M Galemmo. ““LEGO ” Knots”. These proceedings.

[3] T. Verhoeff, K. Verhoeff. “The Mathematics of Mitering and Its Artful Application”, Bridges Leeuwar- den: Mathematical Connections in Art, Music, and Science, Proceedings of the Eleventh Annual Bridges Conference, in The Netherlands, pp. 225–234, July 2008.

[4] T. Verhoeff, K. Verhoeff. “Regular 3D Polygonal Circuits of Constant Torsion”, Bridges Banff: Math- ematics, Music, Art, Architecture, Culture, Proceedings of the Twelfth Annual Bridges Conference, in Canada, pp.223–230, July 2009.

[5] T. Verhoeff. “3D Turtle Geometry: Artwork, Theory, Program Equivalence and Symmetry”. Int. J. of Arts and Technology, 3(2/3):288–319 (2010).

[6] T. Verhoeff, K. Verhoeff. “Branching Miter Joints: Principles and Artwork”. In: George W. Hart, Reza Sarhangi (Eds.), Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture. Tessel- lations Publishing, pp.27–34, July 2010.

[7] B. Ernst and R. Roelofs (Eds.). Koos Verhoeff. Foundation Ars et Mathesis, 2013.


Full Text


intern file

Sonstige Links