Catalog for the Exhibition of Mathematical Art held in conjunction with the 2022 Joint Mathematics Meetings. Descriptions of the works and statements by the artists. Edited by Dan Bach, Robert Fathauer, and Nathan Selikoff. 7.5″ x 7.5″, 100 pages. Now available @ https://mathartfun.com/ExhibitionCatalogs.html
The Octaplex, symmetry in four-dimensional geometry and art, is now available on Elsevier-ScienceDirect @http://bit.ly/JCOctaplex
I was preparing some artwork (The 12-30 project, #211 – July 30 ) for an upcoming exhibit and I clicked the emboss filter – almost by accident. And here it popped up – a next to perfect representation of a (topological) 4D perspective of a Klein bottle – from the outside looking in. Thanks @Mathematica, and thanks #Richard Bennigan for the original script.
The 12-30 project https://jcdigitaljournal.wordpress.com/
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.
The 12-30 project https://jcdigitaljournal.wordpress.com/
December 3. – 337
MathMod & Morenaments. Variation on the Duplin (more likely F. Dupin ) cyclides – named after 19th century French mathematician F. Dupin. Theses surfaces have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems.
The 12-30 project
https://jcdigitaljournal.wordpress.com/
The 12-30 project
https://jcdigitaljournal.wordpress.com/
Moving from JavaView to GeoGebra. Geogebra is a mathematics software designed for mathematics students that creates beautiful visual outcomes. As an anchor to this month’s exploration, I ‘ll use some Sangaku geometry problems from the library of Alex Bogolmony available at cut-the-knot-.org. Sangaku were meant to address two-dimensional geometry problems. Treating the same problems in a 3D environment is bound to bring some unexpected surprises…
This first – sangaku – is called – Three Tangent Circles sangaku. Given three circles tangent to each other and to a straight line, find the radius of the middle circle via the radii of the other two…
October 11 – 284.
The 12-30 project
https://jcdigitaljournal.wordpress.com/
Tri-noid. Tri-noids are part of the k-noid family. A k-noid is a minimal surface with k catenoid openings. The first k-noid minimal surfaces were described by Jorge and Meeks in 1983.
Background: Hubble telescope – a Perfect Storm of Turbulent Gases in the Omega/Swan Nebula (M17)
October 3 – 276
JavaView. Icosahedron. The icosahedron. is a 20-face polyhedron. There are 43,380 distinct nets for the icosahedron. Fifteen golden rectangles span the interior of the icosahedron. These rectangles have 30 edges, and each edge pairs up with its opposite edge to form a golden rectangle. Two icosahedra appear as polyhedral “stars” in M. C. Escher’s 1948 wood engraving “Stars”.
Background – Hubble view of the sunward plunging comet ISON. It was discovered in 2012 by Vitali Nevski and Artyom Novichonok and named after the Russia-based International Scientific Optical Network
October 2 – 275
JavaView. SOAP cube. In mathematics, S stands same sign, O for opposite sign, AP – always positive. The spheres (or bubbles?) in the image map the number and positioning of the vertices.
Background: Hubble View of comet Tempel 1 before outburst. The inspiration for the background came from the enigmatic generic background image – part of the JVR packet.
The 12-30 project 
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