Adalogical Enigmas
Puzzle
G4G13
Pavel Curtis
G13-022
Balance of Power
Puzzle
Arrange the three pieces to create a figure with an axis of symmetry.
G4G13
Rod Bogart
public
G13-023
A Lucky Dissection
Puzzle
A dissection puzzle involving the characters G413.
G4G13
Ben Chaffin
public
G13-024
The Missing 13th
Puzzle
Art
A diecut construction model. Assemble it to discover the missing 13th piece.
G4G13
Roger Gilbertson
internal
G13-025
Pentomino Divination Runes
Puzzle
Magic
A small bag containing twelve square tiles, each with a different pentomino marked on it. Instructions for use in divination are included, along with a set of puzzles using the runes.
G4G13
Alexandre Muñiz
public
G13-026
Laser Cut Pythagorean Theorem Puzzle
Puzzle
Rec Math
A laser-cut puzzle that illustrates a proof of Pythagoras’ theorem. The puzzle pieces either fit in 2 squares aXa and bXb, or in a hypotenuse square cXc. The shapes in the puzzle are taken from a known proof of Pythagoras’ theorem. To my surprise the puzzle turns out to fairly difficult, often taking people about a minute to solve.
G4G13
Gerard Westendorp
public
G13-027
Spectrominoes
Game
Rec Math
This is a paper version of a domino game based on the color addition rules of Al-Jabar designed by Robert Schneider.
G4G13
Ron Taylor
public
G13-028
The Bandaged Cube
Puzzle
An analysis and solution offered in tribute to Professor Erno Rubik and Professor David Singmaster for the 13th Gathering for Martin Gardner.
G4G13
Joseph Cassavaugh
public
G13-029
The High Energy Particle Psychics's Puzzle
Puzzle
Noted high energy particle psychic Fermi Geller is conducting a study of detox particles in his lab. He has successfully generated 13 new particles of Woo-ium in his reactor, but he needs to move the particles into the numerologically stable resonance of the number 13. Can you help him move the particles into the proper alignment?
G4G13
James Stephens
public
G13-030
Marjorie Rice's "Versatile"
Puzzle
Two pages
(1) a description of how to construct Marjorie Rice's "versatile" together with six patches of copies of the tile that will fill the plane by translations.
(2) a sheet with 20 copies of the versatile to copy and cut out in order to discover other ways that the pentagon can tile the plane
Marjorie Rice
G4G13
Doris Schattschneider
internal
G13-032
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
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
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 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
Mechanical Gift
Puzzle
I have gifted an assortment of laser cut acrylic kits of simple mechanisms, including locks, engines, and other such mechanical devices. These were originally designed as physical diagrams for a book project, but are now being produced for sale. Details at http://mechanicalgifs.com.
G4G13
Theodore Gray
public
G13-038
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
G4G13 Latin Square Puzzles
Puzzle
Rec Math
A small collection of Latin square themed puzzles created in honor of the G4G13 conference.
G4G13
David Nacin
public
G13-041
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
Martin Gardner Portrait Maze
Puzzle
Art
Illustration and maze design by Elizabeth Carpenter.
Elizabeth Carpenter
G4G13
Elizabeth Carpenter
public
G13-043
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
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
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
Rainy Day Puzzle Postcards (with the Temporal Logic system called D)
Puzzle
Years ago, when I first learned of the Temporal Logic system called D, I made a puzzle postcard using the system and mailed copies to a few friends. They seemed to enjoy it, so I'm doing it again, for the Gift Exchange.
G4G13
Henry Strickland
public
G13-047
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
How Safe Is It?
Rec Math
Magic
A spectator, with good arithmetical abilities, opens an invisible safe and deposits some invisible coins in it. The magician has the spectator do some arithmetic, receives the final result and then correctly opens the safe and retrieves the correct number of coins, except that the coins are now real!
G4G13
Barney Sperlin
public
G13-051