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Multiplication Tables on Circular String Art lead to Mandelbrot and classic curves

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Thanks to Ed Kellogg for this interesting video link (Times Tables, Mandelbrot and the Heart of Mathematics by Mathologer) and his comments: “This looks like a real treasure trove to me! And not just Mathologer – looks like a lot of other mathematicians or mathematics enthusiasts have put up some great videos since the last time I checked out this area on YouTube! Visually entertaining and illuminating videos illustrating mathematical concepts and processes used to seem almost as rare as hens teeth – nice to see how much that situation has improved.” … I agree, Ed… Looks like I’ll want to spend more time exploring more of his – and related – videos! :-)

Mathologer - String Art Mandelbrot

 

Möbius strips of light … Donald in Mathmagic Land … Golden Ratio Nautilus

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From the backlog of interesting sacred geometry links I’ve been meaning to share, here are three, with thanks to colleagues who shared the links with me so I can pass along to you! :-)

  • Möbius strips of light” … These mathematical structures show up everywhere from M.C. Escher drawings to electrical circuits, but almost never in nature. Now, a team of physicists have shown for the first time that light can be coaxed into a Möbius shape. …” Thanks to Ed Kellogg for emailing these links.
  • Disney Cartoon From 1959 Teaches Sacred Geometry: ” … Donald in Mathmagic Land is a 27-minute educational film featuring the one and only Donald Duck. Released on June 26, 1959, it soon became the most popular educational film ever released by Disney. … ” If you haven’t seen this classic, you might want to watch it – or watch again – even if just for historical reasons; it’s an good very basic introduction (or re-introduction) to the the golden ratio, pentagram proportions, Pythagorean mysticism and a gateway to a more in-depth study of sacred geometry. Thanks to Haines Ely for this link suggestion.
  • Golden Ratio Nautilus: George Hart clarifies common misconceptions about popular spiral shapes (specifically golden ratio spirals) in this interesting video where he sets the record straight … or is that curved? :-)

Golden Ratio Nautilus

 

Interesting geometric links to wrap up 2015

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Aerial photography shadows reveal 8-sided geometry of the Great Pyramid at Giza, Egypt

Hi all:

Here’s a fun and interesting collection of sacred geometry links you might enjoy:

Every year I update this sacred geometry calendar which has images from the Martineau Solar System. Here are details about the 12 images which are highly accurate geometric models of pairs of planetary orbits in our solar system. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence.” Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off.

Martineau solar system calendar -12 months

Martineau Solar System Calendars

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zazzle Martineau solar system calendar -12 months

I just updated this sacred geometry calendar which has images from the fascinating geometric Martineau Solar System models. Here are details about the 12 images which are highly accurate geometric models of pairs of planetary orbits in our solar system. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence in the Solar System.” Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off.

Background Video, Info and Exhibits of the Martineau Solar System

Beading in 3D, 120-cell 3D printed models and more

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Half of a 120-cell (3D printed model)

I received a general question via email from a visitor to GeometryCode.com interested in beading 3-dimensional shapes. Here are the results of my explorations in the process of very quickly researching this question, and my response:

Since your original question was about beading – although many of these may not have geometric aspects of interest – here are some example of 3D beading quite a few example videos of 3D beading that might be helpful.

Since a new dimension is being added (with infinite variations on what can be added to go from 2D to 3D) there are numerous ways to make a 3D pattern from a 2D pattern; these include:

  1. extruding (translation of ) a 2D shape: just making identical copies of the 2D pattern stacked atop each other
  2. rotation or reflection of a 2D shape around either the X or Y (or another axis in the plane of the 2D image)
  3. using other symmetry or symmetries within the 2D object(s) to replicate aspects into the z-axis
  4. countless other variations …

If you already have a 3D image in mind (such as you will find in Sacred Geometry Design Sourcebook on pages 189 (Great Pyramid fold-up model) or Platonic and Archimedean Solids, variations, etc. 196-229 or (space filling polyhedra and close-packing of spheres on page 239, for example) you already have a 3-dimensional pattern to start with. If you have a specific media (such as beading, stained glass, wood-working, welding, Zometool, 3D printing, magnetic spheres, or countless other media variations), you will have other constraints and opportunities to explore. In order to assist further, I would need to know which image on which page in SGDS – since there are over 1300 images in the book! – you have in mind to use for your 3D design.

If you want to make a prototype (or multiple identical copies) you might want to explore 3D printing. There are now somewhat affordable 3D printers, and lots of local 3D printing services. Here’s an example (the “Half of a 120-cell” image on this page) of a 3D-printed geometric shape with kudos to Henry Segerman and Saul Schleimer. Be sure to watch the videos in addition to on this page about the associated images, such as Quintessence (which evidently is also a 3D/4D puzzle/toy which looks wonderful), Triple helix, and Triple gear; fascinating! … and don’t forget to check out the 3D art of Bathsheba who has some exquisite 3D geometric art. :-)