Math-Art series, July update

“Boy singular surfaces” –  Math Art series, vol. 6,  is now available on the AppleStore and on GoogleBooks. A black and white version is also available on Amazon-Kindle.




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.


October 31 – 304.

The Kuen kabuki. In mathematics, a Zoll surface, named after Otto Zoll, is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. The Kuen surface is a special case of Enneper’s negative curvature surfaces

Background: Hubble telescope. Galaxy Cluster MACS J0717, 5.4 billion light-years from Earth. It is one of the most complex galaxy clusters ever seen.


October 27 – 300.

Celebrating image # 300 (65 more to go!) – from – very old (the background tiling) – to very new (the abstract shape)…

JavaView – A periodic minimal surface constructed by German mathematician Karl H. Schwarz using the following two principles:

  1. If part of the boundary of a minimal surface is a straight line, then the reflection across the line, when added to the original surface, makes another minimal surface.
  2. If a minimal surface meets a plane at right angles, then the mirror image of the plane, when added to the original surface, also makes a minimal surface.

Floor tile– same surface taken through a Lagrange spin filter.

Background: Hubble telescope. Incoming Comet ISON. Its glare can be seen at the left bottom of the foreground object.


October 24 – 297.

JavaView – In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Ernst Lebrecht Henneberg, a German mathematician and professor of applied mechanics.

Background: Hubble telescope. Infant stars in the Small Magellanic Cloud


October 21 – 294.

JavaView – The Chen-Gackstatter surface was the first completely immersed minimal torus of finite total curvature, discovered in 1981. It is an isolated surface with one Enneper end.

Background: Hubble telescope. SN 1006 – A ribbon of gas caused by a stellar explosion that occurred more than 1,000 years ago.


October 14 – 287.

JavaView – Triunduloids on a cloud. After H.B. Lawson’s description of a minimal surface whose existence was proven by Nick Kapouleas. From a script by Karsten Große-Brauckmann and Konrad Polthier.

Background: Hubble telescope. Clear Skies on Exoplanet HAT-P-11b.