364+1

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 hermay.org

Wishing you all a wonderful 2016.

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364

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.

363

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.

362

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

361

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.

360

December 26 – 360

MathMod & Morenaments. “Night in Russia”. A Chagall-like shape coming out of a double twist Neovius torus. After an original template by A.Taha.
Background: A pmm symmetry. The sixth symmetry consists of two perpendicular reflections It produces a “double mirror” patterns (pmm)

359

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.