Modern Sangaku

Sangaku are geometrical problems carved on wooden tablets. They were very popular in Japan during the Edo period (1603-1867).

Sangaku was the theme for the 12-30 project, month of November. I compiled the entire series with additional artworks inspired by the Sangaku tradition in one volume including over 60 illustrations, the original geometry they originated from, along with their mathematical description and possible solution

The book is now available in electronic format on the iBook store, GoogleBook, and Kindle. The individual images, large size print on canvas on SaatchiArt.




December 31 – 364+1

MathMod & Morenaments. Cayley cubic. I started the 12-30 project (12 mathematics visualization software/1 program a month/1 image a day in each program) January first, 2015 with a Cayley cubic done in SURFER (plate #01) – I thought it would be interesting to close the loop with a variation of the same equation 12 month later in a different environment. Background a p4g symmetry.

Thank you to all who followed & supported me through this adventure. Your presence was meaningful to me. Next? A book around Springtime to recap the journey, and maybe getting deeper in the 4th dimension – looking outside/in – We’ll see… All images are available for purchase at

Wishing you all a wonderful 2016.


December 30 – 364

MathMod & Morenaments. A Clifford torus script from A. Taha revisited with the first 23 digits of the number “e”. The Clifford torus is a surface in 4-space. It can be flattened out to a plane without stretching. The Euler number or “e” number is an irrational and transcendental number. It is not a ratio of integers or a root of any non-zero polynomial with rational coefficients. Steve Wozniak of Apple fame took it to 116,000 decimal digits.
Background: P6 symmetry. The symmetry group p6 belongs to the hexagonal crystal system and is characterized by 60° rotations.


December 29 – 363

MathMod & Morenaments. One cell of an octahedron x 10 script by A. Taha.
Background: cm symmetry. This group contains reflections and glide reflections with parallel axes. There are no rotations in this group.


December 28 – 362

MathMod & Morenaments. Richmond polar parametric surface from a script by A. Taha. Herbert Richmond was an English mathematician. He discovered this parametric surface in 1904. It is part of a family of surfaces with one planar end and one Enneper surface-like self-intersecting end.
Background: p4m symmetry. It contains rotations of 90 and 180 degrees and also includes reflections. It is found in Egyptian, Persian and Byzantines patterns


December 27 – 361

MathMod & Morenaments. A Sequin toroid from a script by A. Taha, revisited with harmonic numbers.
Background – (Bottom strip and small tiles). A p3m1 symmetry. That symmetry belongs to point group 3m. It has the same total symmetry content and shape, but the motifs differ in orientation.


December 25 – 359

MathMod & Morenaments. The dervish surface is an algebraic surface related to the Togliatti quantic. I reworked the parameters with the number 18 – a very significant number in the Sufi culture.
Background: P31m symmetry. This symmetry group is part of a series of tiling based on the p3 tiling used in many ancient cultures.