Update 01-28

The project images are coming out of the box! The first one is going to Slovenia, the second in Taiwan and the third in Israel. The original work & text can be found on the 12-30 site, category 01-January. Respectively, January 8, January 17, January 19.

12-30-update1-28

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352

December 18 – 352

MathMod & Morenaments. A mirrored Sherk surface. This minimal surface was named after 19th century German mathematician H. Sherk.

Background: Pgg symmetry. Pgg tilings are symmetric under translation

347

December 13. – 347

MathMod & Morenaments. Breathers. Breathers are pseudospherical surfaces of negative curves. Changing the U & V parameters lead up to a Kuen figure (plate #343). This occurrence was discovered by Richard Palais using 3D-XplorMath. Here I explore the shape of the surface in more of a cultural and historical context and as a reference to mathematician E. Beltrami who discovered the pseudosphere in 1868.

Background: pmm symmetry. This symmetry group contains reflections whose axes are perpendicular and has no glide-reflection.

346

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.

344

December 10. – 344

MathMod & Morenaments. A torus seems like a simple surface – a circle revolving about an axis. It is extremely useful in higher dimensional space. It also takes on stranges shapes when parameters U & V are changed.
Background A p3m1 symmetry – In the symmetry group p3m1, reflection lines are perpendicular to the generating translation axis

343

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.

342

12-08

December 8. – 342

MathMod & Morenaments. Breske-novic. The maximum number of nodes on a surface of degree 9 is still unknown… Sonja Breske found this variant of the Chmutov’s surface while writing her thesis. I slightly altered the configuration by inserting a Fibonacci sequence in the first segment of the equation.
Background. P4g symmetry tiling. P4g symmetry is characterized by reflections and both 90° and 180° rotations. It can be found in ancient oriental cultures as well as in several of Escher’s sketches.