Math-Art series

The electronic version of Math-Art, Vol 1 –  Conformal maps – is now available on



Update 05, 2016

The 12-30 project, animated HD for the month of November  “Current Sangaku” – is now on Vimeo. Images of the sequence were originated in Geogebra. Additional credits: Yutaka Yamada, Derek & Brandon Flechter for the music.


December 22 – 356

MathMod & Morenaments. Folium before it evolves in a trefoil curve. A folium is a parametric surface. Descartes put his signature on one, so did Kepler. Because it involves a polar equation – the pedestal on which the main folium stands is a visualization of that same object polar coordinates.
Background: A pgg symmetry. It is characterized by glide-reflections in two perpendicular axes and produces “double glide” patterns (pgg patterns)


December 12. – 346

MathMod & Morenaments.
This 3D parametric surface is attributed to programmer and mathematician Roger Bagula. I slightly extended the x parameter to emphasize the interconnection of the two volumes.
Background: P31 symmetry. This group has three different rotation centers of order three. It has reflections in three distinct directions.


December 11. – 345

MathMod & Morenaments. The Clebsch surface is a non-singular cubic surface studied by mathematician A. Clebsch (1871). Like all nonsingular cubic surfaces, the Clebsch cubic can be obtained by blowing up the projective plane in 6 points
Background: A p4 symmetry. A p4 tiling is symmetric under two- and four-fold rotations.


December 9. – 343

MathMod & Morenaments. The Kuen surface is a special case of Enneper’s negative curvature surface. Beyond its central part, there is a significant structure that seems to appear as phantom spheres.
Background: variation on a p6m symmetry.