Thursday, July 23, 2020

Geometry Links - July 23, 2020

The Mathematics of Neural Networks (Explained Visually)

Origami LED Wall Art

Animation full of optical illusions

Stellarium - night sky atlas, pick a night and track the Heavens moment by moment

Geometric Hokusai from 100 Views of Mt Fuji
Through a Spider Web:
At Sea (note the Escher transformation long before Escher was born):

Paula Pietranera origami and sumie

Susan Hensel "Geometric Stitch” online show

Origami Extravanganza! 
Foldeas: Sharing Ideas through Origami:  "Foldeas is a series of hands-on presentations, each one related–one way or another–to paper folding, by guest speakers from a wide variety of countries. They are cost-free, through the Zoom platform.   Gerardo has invited Leyla Torres (OrigamiSpirit) as the next guest speaker.  Leyla Torres has a wonderful website ( and many new folders have learned from her online videos. 
Saturday July 25, 11:00 - 1:00 pm (New York) / 4:00 - 6:00 pm (London) / 8:30 - 10:30 pm (New Delhi). Limited seating!

"48 Straight Hours of Folding with 48 world-class designers!   One workshop per hour!  It's all on Zoom and you will receive the recordings after the event (phew!).  The fee hasn't been posted yet but here's the link for registration ( and 

"OrigamiUSA has a wonderful program on Zoom (with recording after the event) called OrigamiConnect (  Every season there's a series of workshops available for $10 each.”
hat tip to Lucinda Davis

The life and work of Ruth Asawa

How curved edges affect the wrinkling of ultra-thin materials

Tuesday, July 7, 2020

Geometry Links - July 7, 2020

Square Wave - kinetic sculpture

Difold origami folding bottle

"A Clarified Typology of Core-Periphery Structure in Networks"
"We unpack an often overlooked distinction between hub-and-spoke and layered core-periphery models in empirical network analyses"
Beautiful Twitter thread introduction to the concepts

Wood rock set balancing blocks

Sand drawing robot with 50 miniature servos and two half tanks - large scale “dot matrix” beach printer
Editorial Comment:  Ivan Miranda should talk with Theo Jansen and do this as a strandbeest

Octopus at 1600 meters

"A database of paper airplanes with easy to follow folding instructions, video tutorials and printable folding plans. Find the best paper airplanes that fly the furthest and stay aloft the longest."
hat tip

A Decade of the Sun - "Every second of the 61-minute video represents images taken over a single day, with the first frame showing the sun on 2 June 2010, and the last frame captured on 1 June 2020.”

The Shape of Difficulty:  A Fan Letter to Unruly Objects by Bret L. Rothstein
"an ode to and exploration of these 'unruly objects'—Rubik's cubes, geometric dissections, secret-opening boxes, string disentanglements, and so many more"
Editorial Comment:  The author is a cousin I’ve never met.  He is the first enigmatologist I’ve known of.

Smart Thermally Activated Textiles - robotic fabric

Barbara McKell Art - mandalas

Game engine for non-Euclidean worlds

The Most Important Jigsaw Puzzle

Tuesday, June 23, 2020

Geometry Links - June 23, 2020

"A rose engine lathe is a specialized kind of geometric lathe. The headstock rocks back and forth with a rocking motion or along the spindle axis in a pumping motion, controlled by a rubber moving against a rosette or cam-like pattern mounted on the spindle, while the lathe spindle rotates. Rose engine work can make flower patterns, as well as convoluted, symmetrical, multi-lobed geometric patterns. The patterns it produces are similar to that of a Spirograph, in metal."
I learned about it through this interview with Brittany Cox, an antiquarian horologist and proprietor of Memoria Technica

How to make two far-flying paper airplanes
Every Friday Mahir Cave shows how to make a paper airplane - cool paper planes, from origami easy to complex.
Paper airplanes that fly far are his specialty and his goal is "How to make the best paper airplane in the world.”

Leonardo Criolani - Italian designer
hat tip:

Degrees of Freedom - origami inspired mechanical engineer and his designs

The work of Hadieh Shafie

Gömböc - a shape which has "only two equilibrium points—one stable and one unstable, instead of the usual minimum of 4.  It is self-righting no matter how you set it down."

Flipo Flip™ — Pocket Size Kinetic Skill Toy

Adam Savage's One Day Builds: Rhombic Dodecahedron Infinity Box with Matt Parker!

Isamu Noguchi’s ashtrays

Optical Illusion:  Ninio’s Extinction Illusion - what you see is not what you get

John Kostick’s work on polar zonahedra - be sure to check out the 3D models linked to his paper

Corona Virus
The most important jigsaw puzzle right now is the way the CoV-2 spike, a 3 part structure, attaches to the human ACE2 protein through which it can enter the cells of our bodies and figuring out how to stop it.

FoldIt ( is a citizen science crowdsourcing site on protein folding.  They’ve been up and running for over a decade and currently host a series of CoV-2 protein folding puzzles.  

These two papers, after a cursory search, are the clearest of representations of the spike and the protein I’ve seen:
Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation
Structural basis for the recognition of SARS-CoV-2 by full-length human ACE2

Another way to approach the Coronavirus puzzle may be through sound.  There are sonic representations of the Coronavirus spike made by Markus Buehler ( and his team at MIT.  They translated the 20 amino acids into tones based upon their spectra and used duration and volume to indicate other features like curvature into helices and stretching out into flatness.  

The Sonification of the Coronavirus Spike Protein (Amino Acid Scale) is about 35 minutes long 
( and 
The Viral Counterpoint of the Coronavirus Spike Protein (2019-nCoV) 
( is nearly two hours long and has three distinct movements, (one for each strand of the spike?).

I’ve listened to both and played along with parts of both of them wondering if jamming with the virus could jam the virus or whether noise cancelling algorithms could cancel the CoV-2 spike, that is if the MIT amino acid to sound notation can go from sound to amino acid as well as amino acid to sound.

Naive or crazy as that may sound.

In any case, if you see anything on the Geometry Links of COVID-19 or ACE2, please let me know.  Would be good if we could focus more attention on this critical point, where virus meets human cell, as a whole species conversation because we just might need a whole species conversation right now, and not just on COVID19.

Stay safe, be well.

Tuesday, May 5, 2020

Geometry Links - May 6, 2020

Reuleaux triangles roll like wheels
hat tip:

George Hart’s warped grid jigsaw puzzles
hat tip:

Sandra - kinetic sand sculpture, "a magnet mounted to a 2-axis SCARA mechanical arm to guide a steel ball through a bed of sand, creating an infinite number of patterns"
hat tip:

Shape shifting geometric soft robot

Floating table - a tensegrity
hat tip

Psychedelic hooping

Modernist Sandcastles by Calvin Seibert

Ruth Asawa wire sculptures to become USPS “Forever Stamps"

Shoji Sadao - visionary architect and colleague of R Buckminster Fuller and Isamu Noguchi
hat tip to Joe Clinton

New aluminum metal-organic framework with ultrahigh porosity for storage of hydrogen or methane for vehicles

Toilet paper fullerenes and Charmin nanotubes

Alison Martin’s geometric constructions

Sunday, March 29, 2020

Geometry Links - March 29, 2020

Coloring Workshop: Beautiful Symmetry (Suitable for all ages)
Tuesday, March 31
12:30 pm EST

Alex Berke
Calm yourself with coloring and learn math in the meantime! Join Alex Berke, a creative computer scientist, civic hacker, and MIT Media Lab researcher, to engage with mathematical concepts visually through coloring challenges and puzzles. 

Come ready to color with us! 
Don't forget to bring your favorite coloring tools—your fine point colored pens, crayons, or a pencil you just found.
To participate, download and print out these coloring sheets:

About the Book: Beautiful Symmetry by Alex Berke
Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts.

Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them.

Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.


New 3D-Printed Lattice Designs Are Ultra-Lightweight and Ultra-Stiff

3-D printing glass

Dissecting and redesigning protein-based pattern formation

Tubulane Inspired Ultrahard Polymers

Buckyballs in space made from carbon dust of dying stars

Research reveals key molecular events in crystal growth

New high temperature superconductor, thorium decahydride (ThH10)

Atomic-Level Imaging May Enable Metals With Unprecedented Properties

Crystals that shrink when heated

Degrees of Freedom - origami furniture from a former SpaceX designer

Laser cut steel in nautilus shell forms
hat tip:  @doctorow

Geometry of Circles - 1979 Sesame Street video with score by Philip Glass
hat tip:

Sunday, March 1, 2020

Geometry Links - March 1, 2020

Donald Knuth’s Christmas Lecture on π in the art of computer programming

A crystallographer finally gets her due:  Isabel Ellie Knaggs and the tetrahedral structure of carbon compounds

Hana Hanashi - Flower Story - botanical animation of lifecycle of flowers
hat tip to JPMokray

Change of perspective
hat tip to Bob Toabe

Lego microtonal guitar
hat tip to

New Layered Magnetic Material Has Properties Useful for Twistronic Devices and Spintronics

Crystal stacking process open up new possibilities

“Perfect” solar energy absorber created by laser etching metal with nanoscale structures

New Kirigami (Folded Paper) Designs Support 14,000 Times Their Own Weight

Time-Lapse Shows Bacterial Cultures Form a Flower Pattern

Gold atoms form peculiar pyramidal structure

Logo design statistics
hat tip:  carolina24toro

Sunday, December 22, 2019

Geometry Links - December 22, 2019

Tunable Crystal Symmetry in Graphene Enables Nanoelectromechanical Sensors

Controlling crystal growth for innovations in medicine, engineering

The Fascinating Secret Behind Crystals That Shrink When Heated

Tara Pratap Ebsworth

Neutrinos Lead to Unexpected Discovery in Basic Math

Six(?) sided vinyl record with overlapping tracks

More Edmund Harriss*
*see October 2019 Geometry Links: 
Patterns of the Universe: A Coloring Adventure in Math and Beauty by Alex Bellos and Edmund Harriss

How a Tesla valve works

Flower shapes and pollination analysis
“Modularity increases rate of floral evolution and adaptive success for functionally specialized pollination systems” by Agnes S. Dellinger, Silvia Artuso, Susanne Pamperl, Fabián A. Michelangeli, Darin S. Penneys, Diana M. Fernández-Fernández, Marcela Alvear, Frank Almeda, W. Scott Armbruster, Yannick Staeder and Jürg Schönenberger, 5 December 2019
All morphometric analyses were performed in R and scripts, they are available in file at

Aquatecture rain-catcher

Twixt - pegboard and string connection game reissued
hat tip to

Many ropes and one jumper

Victor Acevedo’s Digital Art Calendar

Optical Illusion of the Year