364+1

The 12-30 project https://jcdigitaljournal.wordpress.com/

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.

364

The 12-30 project https://jcdigitaljournal.wordpress.com/

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

The 12-30 project https://jcdigitaljournal.wordpress.com/

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

The 12-30 project https://jcdigitaljournal.wordpress.com/

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

The 12-30 project https://jcdigitaljournal.wordpress.com/

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

The 12-30 project https://jcdigitaljournal.wordpress.com/

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

The 12-30 project https://jcdigitaljournal.wordpress.com/

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.

358

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December 24 – 358

MathMod & Morenaments. Linoid rewritten as an Egyptian fraction. The lidinoid is a triply periodic minimal surface named after Swedish mathematician & chemist Sven Lidin. The 3D brick, curiously takes on a tiling pattern.
Background: Pmm symmetry. It consists of two perpendicular reflections. characterized by reflections in perpendicular mirrors and produces “Double mirror” patterns (pmm patterns).

357

The 12-30 project https://jcdigitaljournal.wordpress.com/

December 23 – 357

MathMod & Morenaments. “The kiss” – Regrouping Togliatti 31 double points. Togliatti was the Italian mathematician that showed that quintic surfaces have 31 ordinary double points.
Background: Pmg symmetry – This group contains reflections and glide reflections which are perpendicular to the reflection axes. It has rotations of order 2 on the glide axes, halfway between the reflection axes.

356

The 12-30 project https://jcdigitaljournal.wordpress.com/

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)