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.


Update 04, 2016

The 12-30 project is going to Jyväskylä this August!

Left a 16-cell polytope, right a seven symmetry hyperbole. Original plates – the 12-30 project – 05-08, 05-26.



December 5. – 339

MathMod & Morenaments. The flight of the owl. Variation on Maeder’s owl – A minimal surface found by Roman Maeder, author of the book Programming in Mathematica, the standard reference for programming
Background – a pmm symmetry.


December 2. – 336

MathMod & Morenaments. Inspiration from mathematical objects comes in many shapes – Today, a floral pattern from a Henneberg parametric surface – a non-orientable minimal surface named after mathematician Lebrecht Henneberg.

I kept the original visualization – as is – in a reflection on the vase holding the flowers.


December 1. – 335

MathMod & Morenaments – I started the year with SURFER from Imaginary.org. I might as well close the year with the Imaginary.org programming community.

MathMod is a mathematical modeling software. It visualizes and animates implicit and parametric surfaces. It  was created by Abderrahman Taha and is available at SourceForge

Morenaments was created by Martin Von Gagen and is available on the Imaginary.org site. The program creates symmetrical patterns in one of the 17 symmetry groups of the Euclidean space.

The combination of the mathematical objects from MathMod and background patterns Ill create in Morenaments should make for an interesting visual dialog.

Today’s object is a cube-sphere – how to turn a cube into a sphere – which is done by connecting the mesh/vertices from one to the other. I slightly tweaked the script to make them overlap instead of just blending – still an all in one cube in a sphere. I used the Morenaments background to create the drop pattern around and in the spherecube.


November 27 – 331.

Geogebra. This sangaku is intriguing because of the symmetrical aspect of its geometry. It asks to find the diameter of the smallest circle(s) in terms of the central circle(s).