Thursday, December 21, 2017

Geometry Links - December 21, 2017

true/false - algorithmic kinetic light artwork
https://vimeo.com/238066625
Fragments of RGB
https://vimeo.com/21234795
hat tip:  boingboing.net

Peter Dahman paper engineer
https://peterdahmen.de
https://youtu.be/NdXvEXwOEHU
https://vimeo.com/98760774

Cassells' carpentry and joinery - "first written and illustrated in 1854, painstakingly details all of the joinery techniques--many of them forgotten,” free downloadable book
https://archive.org/details/cassellscarpentr00hasl
http://www.core77.com/posts/70349/Free-Downloadable-Book-on-Materials-Processes-Principles-and-Practice-Reveals-Forgotten-Joinery-Techniques

Visualization of Amazonian bird calls
https://vimeo.com/229927018

"Drawing from noise, and then making animated loopy GIFs from there"
https://necessarydisorder.wordpress.com/2017/11/15/drawing-from-noise-and-then-making-animated-loopy-gifs-from-there/

Geometric pies (πs?)
https://www.instagram.com/lokokitchen/
http://www.core77.com/posts/70952/Lauren-Kos-Incredibly-Designey-Pies

Reversible tent design for homeless
https://www.billionbricks.org
https://weatherhyde.org
https://inhabitat.com/reversible-weatherhyde-tent-saves-lives-in-extreme-weather/

Optical illusion
http://www.core77.com/posts/71024/New-Brain-Breaking-Optical-Illusion-These-Lines-are-All-the-Same-Shape

Diffusion Choir - a kinetic sculpture that uses 400 folding elements to reveal the movements of an invisible flock of birds
https://vimeo.com/187037469

Cristian Marianciuc folds and decorates a different origami crane every day, for over 1000 days
https://www.instagram.com/icarus.mid.air/
https://www.treehugger.com/culture/paper-crane-1000-days-cristian-marianciuc.html

Complexity in Nature albums
https://www.facebook.com/steve.lawrence.52/photos_albums

Max Bruckner’s collection of polyhedral models
http://publicdomainreview.org/collections/max-bruckners-collection-of-polyhedral-models-1900/
https://boingboing.net/2017/12/21/max-bruckners-polyhedral-mo.html

Saturday, November 25, 2017

The 25 Interrelations of the Platonic Solids

Once upon a time, back in the first years of the 1970s, I saw a page in Keith Critchlow's Order in Space that showed all 25 interrelations of the Platonic 5 Solids (tetrahedron, hexahedron or cube, octahedron, pentagonal dodecahedron, and icosahedron) and how they fit inside each other.  Over the years, I built all 25. 



I've also made magnetic models of some of these structures but not all of them and the nets are not all perfect but I did my best.  A couple of times I've tried to send these nets to Critchlow but they were returned unopened.  Oh well.

As with the Quanta Set that make up the Platonic Solids (http://geometrylinks.blogspot.com/2017/11/4-symmetrical-tetrahedra-of-5-platonic.html), I'd like see these built as class 2 tensegrities with spherical magnets at the vertices.





The following are the nets of the 28 different polyhedra that comprise the 25 Interrelations of the Platonic Solids.



Tetraset


 HexaSet.1


















HexaSet.2





















Octaset



DodecaSet





















IcosaSet.1


IcosaSet.2












Update:  Originally, I transposed the tetra in dodeca net with the octa in dodeca net.  The mistaken nets are below:

 


 




Thursday, November 16, 2017

4 Symmetrical Tetrahedra of 5 Platonic Solids


This is a video of a magnetic model of the Cube and the Tetrahedron broken down into its smallest symmetrical tetrahedra, what Buckminster Fuller called the A and B Quanta or mathematicians call Schläfli orthoschemes (I think).

The A and B Quanta make the equilateral triangle Tetrahedron (4 sided solid), square Cube or Hexahedron (6 sided), and equilateral triangle Octahedron (8 sided)

The A Quanta is 1/24th of a Tetrahedron, the smallest symmetrical tetrahedron to make up a Platonic solid.  Here is the net of the A Quanta which can be folded to make the left and right hand versions, both of which are needed.
                                                                           



                                                                                                                                                                             
The B Quanta plus the A Quanta makes the Cube or Hexahedron 
and the Octahedron,
two other Platonic solids
48 A Quanta + 24 B Quanta = 1 Cube
2 Cubes = 1 Octahedron


 




                                                                                                                                                                                   






A third, the Dodeca Quanta, builds the Dodecahedron

120 Dodeca Quanta = 1 Dodecahedron



And a fourth,
120 Icosa Quanta = 1 Icosahedron  












I've made magnetic models of the 5 Platonic solids with the magnets in the centers of the faces of the polyhedra.  The A and B Quanta have the same volumes and I suspect share that volume at the same scale, all four tetrahedra share one common right angle triangle, but I haven't tested that hypothesis.

Since I saw this video, I think the next model should be a set of these Quanta built as class 2 tensegrities with ball magnets at the vertices.  In fact, I'd commission someone to build it, for the right price.
                      


Wednesday, November 1, 2017

Geometry Links - November 1, 2017

360º Book

The Eyeballing Game

Transforming paper sculptures (kami kara)

Visual math made with laser cutters
hat tip John Robb of Global Guerrillas

Don’t Fall for Babylonian Trigonometry Hype
Since I forwarded the hype, I now forward the rebuttal.  Personally, I believe it’s turtles all the way down or, as the little old lady said, “If G*d had wanted us to fly, He wouldn’t have given us the railways.”

Fibonacci series animation

3-D Printed Self-Folding Electronics

Victor Acevedo’s Instagram showing his geometric art

Numericons - vector tiles for graphics, logos, patterns, and design, soon to be 10 sets of 100 tiles each

Tensegrity
You can touch this tensegrity art
Tension Designs

Synergia - origami pavilion

Zenth - a 3D labyrinth

Truth to Tools - from point and circle to try square, straightedge, dividers etc. 

John Hiigli (1943-2017) died 18 October 2017. A memorial service is being planned for November 11.  
See John's Facebook page for details https://www.facebook.com/john.hiigli44
John's work at http://www.johnahiigli.com

Thursday, August 24, 2017

Geometry Links - August 24, 2017

Murmuration chandelier
hat tip treehugger.com

Frederike Top’s geometric lights and constructions

Calvin Siebert’s sand castles
hat tip CBS Evening News (!)

2500 year old earthquake proofing

Generative art by Hyperglu

The geometry of plant forms - fractals, Fibonacci series, and the sacrament of geometry
hat tip Marjorie Farrell

Mandala stones

What’s a humbug?

Portable teahouse made from folded paper - I wonder what Rikyu, the great tea master, would have thought.  He once built a teahouse out of gold for and with the Shogun.

Auxetic structures

Star - lighting installation
More from Planetary Folklore

Gabriel Schama - laser cut wood designs and more

Babylonian trig table

Monday, July 17, 2017

Geometry Links - July 17, 2017

Geometry of theory space - conformal field theory, amplituhedron, and bootstrap physics
https://www.quantamagazine.org/using-the-bootstrap-physicists-uncover-geometry-of-theory-space-20170223/
Amplituhedron
https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917

Best of Galaxies
https://twitter.com/BestGalaxyPics

Woodswimmer
https://vimeo.com/196683500

4D Monkey Dust
https://youtu.be/RhuaPhahHbU

Permutations of the 9 panel comic grid
https://math.stackexchange.com/questions/2287784/in-how-many-different-ways-can-a-9-panel-comic-grid-be-used

Eirik Brandal - interactive electronic sound sculptures
http://eirikbrandal.com
Composition #11
https://youtu.be/dKOnTziBtLM

Pufferfish geometers
https://youtu.be/ee3GIPoLe6c
hat tip Zann Gill
Editorial Comment:  Are crop circles made by invisible, terrestrial or aerial pufferfish?

Hannu Huhtamo light art photography
http://www.hannuhuhtamo.com/light-art-photography/
https://www.facebook.com/HannuHuhtamoPhotography/

Detailed map of human brain “white matter"
http://www.bbc.com/news/health-40488545

Ten Fold Engineering
The Levers:  https://youtu.be/RQi6gXZHyAc
Demonstrator Unit:  https://vimeo.com/193884074

Bast Cat Furniture
https://www.instagram.com/bastcatfurniture/

Benefit reception and screening of film to preserve Falmouth, MA Fuller Dome 
https://www.capenews.net/falmouth/news/plans-for-historic-dome-receive-outpouring-of-support/article_1a0ccca5-933c-5540-b8c7-6b7efad85322.html

The organization will hold a benefit reception and film screening on Saturday, August 5, to raise money for the project.

Ms. Nicole Goldman said that Mr. Fuller’s daughter, Allegra Fuller Snyder, who is nearly 90 years old, will be present at the event. Ms. Fuller Snyder is co-chairman and founder of the Buckminster Fuller Institute.

A cocktail reception will take place at the home of Catherine Cramer at 50 Buzzards Bay Avenue from 4 to 6 PM. A screening of “House of Tomorrow,” written and directed by Peter Livolsi, will take place at the WHOI Redfield Auditorium on Water Street at 7 PM. The screening will be followed by a question-and-answer period with Mr. Livolsi.

Tickets for the benefit reception cost $50 per person, and tickets for both the reception and film screening cost $75 per person. Those who attend the reception will receive preferred seating at the screening. Tickets for the film screening alone can be purchased through the Woods Hole Film Festival.

Those wishing to attend can make a reservation by e-mailing info@artdome.org or calling Ms. Goldman at 978-505-5978.

Tickets are available through Eventbrite.com, or checks payable to The Dome for Contemporary Arts c/o ArtsFalmouth may be mailed to PO Box 136, Falmouth, MA 02541.

Saturday, June 17, 2017

Geometry Links - June 17, 2017

Carbon fiber pavilion woven by robots and drones
https://www.treehugger.com/green-architecture/drone-robot-woven-carbon-fibre-pavilion-icd-itke-university-stuttgart.html
https://vimeo.com/icd/rp2016-2017

Abdelaziz Nait Merzouk tiles and honeycombs

John Baez geometry

Collective Paper Aesthetics - cardboard and paper modular building systems

Josie Lewis geometric art

Myoshka really likes Greek meander patterns

Image of magnetic “bridge” between galaxies
hat tip Leela Corman

Frederik Vanhoutte's generative graphics

Nanoscale cell image - the research is on lipids but the figures show a detailed look at cell structure

Organic geometry by José Bernabé

Birdland by George Hart

World’s largest kaleidoscope - a rebuilt grain silo

John Edmark - spiraling patterns
hat tip John Belt

Lyman Whitaker - wind sculptures

Monday, May 1, 2017

Geometry Links - May 1, 2017

Business card Level 3 Menger Sponge at MIT and around the world
Jeannine Moseley did a folding session on the Menger Sponge with the Philomorphs once upon a time

John Coltrane and Geometry
hat tip to Steve Provizer

Camboo - bamboo pavilion for Phnom Penh

Constructive Interference - static-kinetic sculpture

Ornitographies by Xavi Bou

NASA’s space fabric - 4D printing, they say

Collatz Conjecture visualizations

Nick Cave’s Until at MOCA
Casey Curran’s kinetic sculptures

Seeing Theory - a visual introduction to probability and statistics

Buddy James visualizes the Dougherty Set
Hat tip to John Higli

The graphical language for the aliens in the film “Arrival”
Painting by Martine Bertrand upon which the language is based
Editorial Comment:  The film is well worth seeing and the team designed about 100 symbols and a methodology to create more.  Might be interesting to imagine such a language not only graphically but also sculpturally as well, a material speech.

Friday, April 7, 2017

Geometry Links - April 8, 2017

Traditional Japanese wood joints cast in glass
http://www.core77.com/projects/63231/Traditional-Japanese-Wood-Joinery-Cast-in-an-Untraditional-Material-Glass

International Cloud Atlas

Fictional flight over actual Mars - natural geometries of another planet

Quintetra Blocks making of video
More Kosticks videos

M.C. Escher: Adventures in Perception
Metamorphose:  M.C. Escher

Stickbulb - LED lights in straight line configurable designs

Tetrahedral hydroplane yacht design

Patterns - short video and director’s notes

Prince Rupert’s Cube

Beauty of Science - “We make beautiful science videos”

Inuit floating maps
Seeing these reminded me of Polynesian stick maps

Geometric Illuminations

Friday, March 17, 2017

Geometry Links - March 17, 2017

Tying It All Together - Youtube channel on knots and braids

Mandala of Light

What machine learning looks like

Infographics of WEB DuBois

Father Magnus Wenninger (1919-2017) who made models of all seventy-five so-called uniform polyhedra died.
His obituary may be read at
http://www.saintjohnsabbey.org/news/benedictine-monk-known-his-math-contributions-dies/

Joe Clinton produced a 14 minute biographical sketch of Father Magnus at
https://vimeo.com/127784023
"A Visit with Magnus" trailer (4 minutes)
https://www.facebook.com/A-Visit-With-Magnus-1523593614521677/

Dwitter - javascript one-liners (must be 140 characters or less) that display pretty animated graphics that you can edit

Paleobiology Database Navigator allows exploration through space, time, and taxonomy

NYC Metropolitan Museum of Art searchable 440,955 record collection online

Eugene Atget.Photgrapher - documenting Paris from late nineteenth to early twentieth century
Article
MOMA collection of his work

Sacred Geometry photo exhibit until April 15, Anise Gallery, London

Daytonian in Manhattan - "The stories behind the buildings, statues and other points of interest that make Manhattan fascinating."

Thursday, February 16, 2017

Friday, January 6, 2017

Geometry Links - January 6, 2017

George Hart’s sculpture “Champy"
https://youtu.be/EX90o65zGEM

Murmuration with sound
https://youtu.be/V4f_1_r80RY

Vitaliy (Volt) Agapeyev
https://www.flickr.com/photos/58607182@N05/

Mondrian Puzzle
https://youtu.be/49KvZrioFB0

Strictly Paper Blog
http://strictlypaper.com/blog/
Laser cut paper stained glass
http://strictlypaper.com/blog/2016/11/new-intricate-stained-glass-windows-from-colorful-laser-cut-paper-eric-standley/

New Kosticks video - Dissecting a Playdough Rhombic Dodecahedron with Miles
https://youtu.be/eYgpXpc0XxM

Solstice:  An Electronic Journal of Geography and Mathematics - they were good enough to include Geometry Links so it is only symmetrical that I include them here
http://www.mylovedone.com/image/solstice/win16/
http://www-personal.umich.edu/%7Ecopyrght/image/solstice.html - Solstice issues from 1990 to present

New technique for revealing characteristics of photonic crystals
http://scitechdaily.com/new-technique-reveals-internal-characteristics-of-photonic-crystals/
http://advances.sciencemag.org/content/2/11/e1601591.full

Carl Fasano’s work
https://vimeo.com/124064560

We Want to Learn
https://wewanttolearn.wordpress.com/category/work/

Peter Kogler’s warped spaces
http://www.kogler.net

Geometric garden by Gabriel Orozco in South London
http://www.southlondongallery.org/page/gabriel-orozco-garden
http://inhabitat.com/gabriel-orozco-designs-mesmerizing-geometric-garden-for-the-south-london-gallery/