1 to 8 Squared
Puzzle
Rec Math
A polyomino packing puzzle with 8 pieces ranging in size from 1 to 8. The main goal is to create a 6x6 square. Further goal shapes (and solutions) can be found on https://www.jaapsch.net/g4g/g4g13.htm
G4G13
Jaap Scherphuis
public
G13-018
12...N Polygons for Plane Tiling
Puzzle
Rec Math
I made pentagons of edges whose lengths are 1,2,3,4 and 5 in order and can be tiled the flat infinitive plane. And also hexagons of 1,2,3,4,5,6 edge length. A set of a few of them is my exchange puzzle.
G4G13
Yoshiyuki Kotani
public
G13-019
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
13 Sided and Suits Dice
Game
Game, Toy, Rec Math
This pair of unique dice consists of a 13-sided die with both numbers and face-card labels for J, Q, K, and A, along with a 4-sided die with the standard playing card suits.
G4G13
Robert Fathauer
Henry Segerman
public
G13-082
4 x 13
Game
Art
Recreational Math
There are 52 cards in a standard deck of playing cards: four suits of 13 cards each. To design a deck of cards, one needs to establish the four suits, each with its own symbol and/or concept, and find a logic for generating the 13 cards in each suit, usually related to the numbers from 1 to 13. My exchange gift is a booklet summarizing my progress to date in designing a set of playing cards based on ideas that Martin Gardner wrote about in his books and columns. The talk corresponding to this item can be found here: <span><a class="in-cell-link" href="https://www.youtube.com/watch?v=ZijlID83FTg&t=15s" target="_blank" rel="noreferrer noopener">https://www.youtube.com/watch?v=ZijlID83FTg&t=15s</a></span>
G4G13
Margaret Kepner
G13-020
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
A Collection of Match Stick Puzzles
Puzzle
Game
Every week at my School's math club, we have one puzzle to solve based around match sticks. My gift exchange item will consist of a small booklet containing 21 match stick puzzles ( in honor of Martin Gardner being born on the 21st of October), as well as a collection of match sticks to solve the puzzles with. The match sticks will have the ends cut off so that there is no danger of fire.
G4G13
Nathan Gaby
public
G13-010
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
A Figurative Tree
Art
Artwork of a low-resolution figurative tree.
G4G13
Robert Bosch
public
G13-075
A Flexier Hexaflexagon
Puzzle
This is a standard trihexaflexagon with some extra crease lines. Cut it out and fold it up in the usual way, using tape or glue, adding the extra creases. The new degrees of freedom allow the hexaflexagon to swim along itself like Escher's fish, as demonstrated three-quarters of the way through my short video "Flexagon Secrets Revealed 1" at
https://www.youtube.com/watch?v=bVJcEJ4vx8U
(see 03:20 and beyond). Would this move work with a rigid network, or does it hinge (pun intended) on subtle properties of physical paper? I don't know!
G4G13
Jim Propp
public
G13-036
A Gift of the Number 13 for G4G13
Rec Math
Science
Participants will receive one spruce cone along with instructions on how to read the number 13 in it.
G4G13
Joe DeVincentis
public
G13-094
A Lucky Dissection
Puzzle
A dissection puzzle involving the characters G413.
G4G13
Ben Chaffin
public
G13-024
A Sliding Block Puzzle App
Puzzle
The app is no longer functional
G4G13
Duane Bailey
Daniel Yu
internal
G13-021
A Small Book of Poetry
Word Play
In 1962 Martin Gardner published an article about a remarkable poem. As far as I know, his is the only scholarly article that has ever been published pertaining to this poem. There is a rich and particular connection between poetry and the more popular topics that are typically covered at the Gardner meetings. Prose and the other literary art forms do not seem to share this connection. Douglas Hofstadter, for instance, has always been especially interested in poetry. This month (March, 2018) the following appeared in the NY Times: "[Ada] Lovelace, ... who was the daughter of Lord Byron, the Romantic poet, had a gift for combining art and science ... She thought of math and logic as creative and imaginative, and called it 'poetical science.' "
Langdon Smith
G4G13
Robert Orndorf
public
G13-045
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
Adalogical Enigmas
Puzzle
G4G13
Pavel Curtis
G13-022
Antimatter Mazes
Puzzle
Game
You are trapped in a maze with antimatter! Your goal is to escape the maze without creating an enormous explosion.
G4G13
Bob Hearn
public
G13-004
Balance of Power
Puzzle
Arrange the three pieces to create a figure with an axis of symmetry.
G4G13
Rod Bogart
public
G13-023
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
Cause to Wonder
Rec Math
A lighting fast calculation trick- good for the not brilliant to seem brilliant and the youngster to be motivated to mentally calculate. It will be printed on paper and I will bring it with me.
G4G13
Lina Menna
public
G13-046
Cavalieri Content Cups
Art
Recreational Math
Just as 13 breaks up nicely as the sum of 8 and 5, so too does the (volume of a) cylinder break up nicely as the sum of a cone and hemisphere, a fact we have seen demonstrated at previous Gatherings in vivid ways. But the one-diagram proof of this partition using Cavalieri's principle is remarkably flexible, as the non-standard Cavalieri Content Cups to be distributed will show. For more information, see v.gd/stinf.
G4G13
Glen Whitney
G13-048
Chinese Tangram
Puzzle
It combines a deck of playing cards, tangram puzzle illustration, folk games (Chinese zodiac) in one set.
G4G13
Wei Tai
public
G13-081
Chiral Icosahedral Hinge Elastegrity’s Geometry of Motion
Art
The Chiral Icosahedral Hinge Elastegrity resulted from a Bauhaus paper folding exercise, that asks material and structure to dictate form. The key new object obtained in 1982 involved cutting slits into folded pieces of paper and weaving them into 8 irregular isosceles tetrahedra, attached along 24 edges, to 12 right triangles, that in pairs form elastic hinges, creating an icosahedral shape held together by elastic forces. The chiral icosahedral hinge elastegrity has noteworthy physical and geometric properties.
At G4G12, shape-shifting through further folding of the hinge elastegrity was presented. It led to a number of familiar geometric objects, as well as some new ones. It can flatten into a multiply covered square, morph into shapes with the vertices of each of the Platonic shapes, model the hypercube, as well as morph into new figures with the vertices of figures of congruent faces that are not regular polygonal regions. With the help of co-presenter professor Thomas Banchoff, we generalized a unique new monododecahedron that had been obtained through folding, into a family of monododecahedra using analytic geometry.
For G4G13 the proposal is to present the Geometry Of Motion of the Chiral Icosahedral Elastegrity. At rest the icosahedral hinge elastegrity has 6 openings framed by the 12 hinged triangles, that form gates that open and close, with a set of orthogonal axes going through their center and the structure’s center. As the structure contracts into an octahedron, the gates close, and the tetrahedra pivot so that the 3 orthogonal axes extend thought the vertices of the octahedron. The gates open maximally when the structure expands back into a regular icosahedron. As the structure gyrates expanding into a cuboctahedron the slits close becoming 6 diagonals of the 6 squares of the cuboctahedron.
The asymmetrical tetrahedra move along a second set of 4 axes that gyrate around the center of the structure. When two tetrahedra are pressed together, along any of the 4 axes, all 12 hinges are activated simultaneously, contracting the 8 asymmetrical tetrahedra chirally, spinning isometrically in unison along the 4 rotating axes, moving towards the center of the structure, into an octahedron. When any two asymmetrical tetrahedra are pulled away along one of the 4 axes, the hinges activate the entire structure extending the 8 tetrahedra spinning in unison with reverse chirality, along the 4 axes that rotate in reverse direction, pivoting around the structure’s center, into a cubeoctahedron.
When external forces are removed, elastic forces in the hinges return the structure into its original regular icosahedral shape.
G4G13
Eleftherios Pavlides
public
G13-095
Crocheting Hyperbolic Regular Octagon and Pair of Pants
Art
Giving a little history and step by step instructions on how to crochet regular hyperbolic octagon with 45-degree angles.
G4G13
Daina Taimina
public
G13-104
Does the Barber Shave Himself?
Puzzle
Word Play
Bookmark with philosophiocal logic puzzle.
G4G13
Delicia Kamins
public
G13-091