13 Serpentine Symmetries
Art
Rec Math
A full-color printed card showing and explaining Serpentine Symmetries, a beaded jewelry set that illustrates the 13 wallpaper groups compatible with bead crochet rope. Serpentine Symmetries was part of the 2018 Joint Mathematics Meetings Exhibition of Mathematical Art, and is one of many complete symmetry samplers in fiber arts that will appear in my G4G13 talk.
G4G13
Susan Goldstine
public
G13-072
Sculptural Martin Gardner
Puzzle
Art
MG Legacy
My contribution to the gift exchange is a 5 X 7 inch, four-color, tri-fold glossy card with photographed imagery of my 11 X 12 X 9 inch multifaceted-portrait-sculpture of Martin Gardner. My painted, kiln-fired, stained glass and stainless-steel-mirrored sculptural portrait includes my image of "Gardner Rabbit", four puzzles and two encoded words.
G4G13
Bronna Butler
public
G13-071
Poly-Twostors Periodic Table, Catalog of 3D Printer Models
Art
Rec Math
It is a classification of 3D Tori. This catalog consists of 14 page which lists the Poly-Twistor models updated in January 2018.
G4G13
Akio Hizume
public
G13-070
PiTop
Art
Rec Math
Pi is certainly one of the most important numbers in mathematics, physics, engineering and, indeed, in all scientific and even some artistic subjects. I have developed a new object which makes Pi tangible in novel tactile, acoustic and visual ways. The PiTOP is a right circular cylinder made out of brass with ratio of radius r to thickness t equal to pi. Because of this design, when spun the object also precesses (or rolls) for a rather long time, leading to an ever increasing precession frequency as it falls, producing what is sometimes called a "finite time singularity". The resulting sound and interplay of ambient light with the PiTOP is intriguing to the ear and delightful to the eye which also results in a strong "motion after effect" illusion. In this presentation I will talk about the development of the object, and demonstrate its physical and mathematical properties.
G4G13
Kenneth Brecher
internal
G13-065
Ace of Spades
Art
My gift is an Ace of Spades personalized with a unique image that combines the G4G logo together with a symbolic representation of Panamanian culture.
G4G13
Jeanette Shakalli Tang
public
G13-063
Waking Up a Student and Seeing Nobody
Art
Martin Gardner suggested the best way to wake up a student and Lewis Carroll woke up many students with his book Alice's Adventures in Wonderland.
Our gift, a microfiber cloth, presents some of Martin Gardner's and Lewis Carroll's words together with a couple of graphical mathematical designs, including a space-filling design created by Julian Ziegler Hunts and a portion of a 12-pointed star created by Amina Quraishi.
G4G13
Nancy Blachman
Bill Gosper, Howard Cannon
public
G13-058
G4G13 Clock Face
Art
Rec Math
A clock face showing the logo for G4Gn at the nth hour, for n=5-12, and the G4G13 logo in the center, and miscellaneous MG items for hours1-4.
G4G13
Skona Brittain
public
G13-057
4-gons and 13-gons
Art
A circle sticker with an image of a hyperbolic tiling of 4-gons and 13-gons.
G4G13
Roice Nelson
public
G13-053
The 13-Zone System
Art
A zometool-based geometrical model/puzzle based on the 13-zone system, i.e., 3 blue lines, 4 yellow lines and 6 green lines, which are associated with the face centers, vertices and edge centers of the cube.
Marc Pelletier
G4G13
Paul Hilderbrant
Amina Bühler-Allen, Michael Stranahan, Scott Vorthmann
public
G13-049
Postcard and Tiny Piece of Equilateral Tridecagon Tiling
Art
Rec Math
I prepared postcards and tiny pieces of "Equilateral Tridecagon Tiling" for the Gift Exchange.
G4G13
Masaka Iwai
public
G13-044
Martin Gardner Portrait Maze
Puzzle
Art
Illustration and maze design by Elizabeth Carpenter.
Elizabeth Carpenter
G4G13
Elizabeth Carpenter
public
G13-043
Catalan Solid Net for further play
Puzzle
Art
The included piece will be a decorated deltoidal icositetrahedron net, which can be colored and subsequently cut and assembled. Alternatively, those with a cutting machine can cut the closed regions on each face of the polyhedron to obtain an interesting polyhedron once assembled. The piece is a prototype for a battery operated votive holder that can be cut using a laser cutter.
G4G13
Carolyn Yackel
public
G13-042
Geometry in Five-Dimensions: Building Quasicrystals from Penrose Tiling
Art
No-one really knows what quasicrystals look like. But we do know, from the diffraction patterns of X-ray crystallography, that they bear a resemblance to Penrose tiling. By combining artistic exploration with mathematical insight into the five-dimensional nature of Penrose tiling we have begun to visualize the structure of quasicrystals.
We are building mathematically precise sculptures of Penrose tiling raised up to a dimension of somewhere between 2 and 5. We have also devised algorithms to explore two-dimensional aperiodic tilings using color and perspective. These drawings sometimes reveal structural patterns that become sculptures.
In January we built a mirrored glass and copper sculpture that attempts to reconstruct the crystallographic origins of Nobel prize winner Dany Schectman’s famous five-fold diffraction patterns.
G4G13
Deborah Coombs
Duane Bailey
public
G13-040
A Fair Die of 13 Faces
Art
Rec Math
A cube is used as a fair die of 6 faces. However, there are many dice of different shapes on the market. To make them fair, most of them usually have some symmetric shapes. I classify these variants of dice on the market into two groups. First, let's consider that a sphere as a model of a fair die with infinity faces. Based on this model, many symmetric shapes can be modeled as dice obtained by caving spheres. We also have a familiar fair device; a coin. That is, a fair coin can be seen as a fair die with 2 faces. However, a real coin has a thickness, and hence it is, in fact, an unfair die with 3 faces. From this viewpoint, I propose a way for designing a fair die with n faces for arbitrary n. I also prepare fair dice with 13 faces as an exchange gift of G4G13.
G4G13
Ryuhei Uehara
public
G13-035
G4G13 Logo Design
Art
Rec Math
This configuration of thirteen sets of concentric circles grows out of an ancient tradition of visual alchemy. The faculties of imagination and intuition are employed as guides in the discovery of new and meaningful relationships between geometric elements in a plane (on a flat surface). In this particular instance, the task was to discover a pattern representing the number 13 wherein harmonic symmetry is a constant. This configuration of thirteen color-coded circular rings answers this design challenge. Logic is also employed as part strategy in the creation of this pattern; a perfect example of the rich dialogue between right and left hemispheres of the brain. Let us remember that Mandalas are intended as two dimensional re-presentations of (ideally sacred) sounds.
G4G13
Vandorn Hinnant
public
G13-034
Tridecahedron Net
Puzzle
Art
This net is similar to those in my 'Cubes and Things' 3D coloring books, where I use playful patterns to accent symmetries of polyhedra. By truncating one vertex of a dodecahedron, it becomes a tridecahedron. (Do you think truncating all the corners would reveal G4G twenty times?)
The theme of 13 is repeated in the sets of joined circles, which were inspired by this year's Gathering 4 Gardner Logo. There are 4 slightly different sets of 13 dots, each in its own color. 4 vertices have 3 circles of 3 different colors meeting. Those 2 sets of 4 vertices mark how 2 tetrahedra could fit into the shape or they can be seen as the 8 vertices of a cube. The 6 large colored areas were accented to also show the orientation of a cube in this shape.
G4G13
Stacy Speyer
public
G13-033
The Missing 13th
Puzzle
Art
A diecut construction model. Assemble it to discover the missing 13th piece.
G4G13
Roger Gilbertson
internal
G13-025
Spiram Siderum
Art. Magic/Illusion, Toy, Science
A craft kit with all parts needed to crate a tiny kinetic sculpture based on the physics of equilibrium, magnetic force, and angular momentum.
G4G13
Raymond Hall
public
G13-015
Tensegritiy Pop-up
Art
Rec Math
In each envelope there will be Kenneth Snelson-like tensegrity flattened inside. As you pull it out, it will pop up to a 3D sculpture.
G4G13
Robert Connelly
public
G13-003
Motley Cube
Art
Rec Math
Six identical sheets to cut out and assemble to make a colorful transparent model of a Motley Cube - a cube dissected into the minimum number of rectangular blocks such that no two blocks are both bounded by the same two parallel planes. In other words, it is delightfully irregular everywhere. This model accompanies the gift exchange paper on Motley Dissections that I am also submitting for the exchange.
G4G13
Scott Kim
public
G13-002
Sakura Pythagorean Tree
Art
Inspired by the Pythagorean Tree in a plane, I stitched the Sakura Pythagorean Tree on a temari ball of diameter 58 cm. This Pythagorean tree has order five and begins with a square of side 5 cm. Upon the first square I constructed two squares to depict the Pythagorean theorem, and from there I continued recursively. Each square is scaled down by a linear factor of about 0.7.
G4G14
Marcela Chioresw
G14-064
Winning Ways HexaFlexagon
Puzzle
Art
Toy
Sadly, all within 13 months of each other, the three authors of the iconic book Winning Ways for Your Mathematical Plays passed away.
Elwyn Berlekamp: Sept 6 1940 – Apr 9 2019
Richard Guy – Sept 30 1916 – Mar 9 2020
John Horton Conway: Dec 26 1937 – Apr 11 2020
All three were friends with Martin and were regulars at the Gathering. Their legacies are grand, and their presence will all be missed.
G4G14
Sean Graves
G14-058
Penrose P3
Puzzle
Art
Recreational Math
I am making paper flexagons with Penrose patterns on them to illustrate the patterns. My stuff touches three things from Martin Gardner, Flexagons, Penrose Tiles, and Polyominos (the classification system for tetraflexagons is based on these with a minor redefinition of polyomino).
See demostration: <a href="https://youtube.com/shorts/HUFKLH3Igqo">https://youtube.com/shorts/HUFKLH3Igqo</a>
R2D3 Designs R2D3 Deseigns
G4G14
Red Deupree
G14-049
Abstract Photograph - Acura TL
Art
Recreational Math
One of my interests is abstract photography, using ordinary photographs as the “paint” and using spatial and mathematical transformations to create an image from one or more sources. One transformation that I’ve been exploring is “Inside Out”, which involves moving the center of the image to the outside and moving the edges of the image to the center. For some source images, the result is a pleasing abstract that doesn’t immediately resemble the source but which contains recognizable elements of the original when you look closely.
G4G14
David L. Kahn
G14-048
The 14 Two-Color Frieze Symmetries in Mosaic Knitting
Art
Recreational Math
Mosaic knitting, a relatively new form of two-color knitting, has become popular because it is easier for the knitter than most traditional forms of color work. The price of this ease is an unusual set of restrictions on color placement for the pattern designer. Carolyn Yackel and I have researched the impact of these constraints on the symmetries of knitting patterns, culminating in a classification of the color-swapping symmetry groups possible in mosaic knitting.
G4G14
Susan Goldstine
Carolyn Yackel
G14-040