Golden Magic
Art
My artwork, 'Golden Magic', especially created for G4G13 conference is dedicated to four remarkable men: Martin Gardner, Raymond M. Smullyan, Tom Rogers, and Al Seckel. Rich in golden mean proportions the composition consists of 13 elements placed inside a Penrose rhomb (P3 Penrose tiling) and displays an interplay of Penrose tiles (from P2 and P3 Penrose tilings), golden (Robinson) triangles, additionally decorated by a fractal pattern. Our minds' eyes can also be amused by certain optical instability.
G4G13
Teja Krasek
Scott Hudson de Tarnowsky
public
G13-110
The Tax Man Problem
Puzzle
Bill Gosper shared this problem with me. He calls it the Tax Man Problem. In the province of Peculia Pecunia, you are paid on an annular basis. That is, you get a (unit radius) gold disk from whose center is punched a smaller disk which you donate to charity. The tax man chops off the largest segment he can, and you get the rest. What radius should you donate to charity to maximize your take home pay? You can use calculus to solve this problem, or you can do it the easy way. Bill joins me in a video on mathwithjames.com where we show you how.
G4G13
James Lee
public
G13-109
The Shifting Maze
Puzzle
Toy
A maze on a flexagon, where the faces keep getting rearranged, adding an additional challenge to finding your way through the maze.
G4G13
Scott Sherman
public
G13-107
untitled (mobius strip)
Puzzle
Art
G4G13
unknown unknown
public
G13-106
The Spikey Sculpture Kit
Puzzle
Art
Assemble a paper sculpture of the Wolfram logo, affectionately known as "The Spikey".
G4G13
Stephen Wolfram
public
G13-105
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
untitled (geometric ball)
Art
Toy
G4G13
unknown unknown
public
G13-103
untitled (optical illusion)
Art
Toy
G4G13
unknown unknown
public
G13-102
The Book of Why Postcard
Science
This item is a postcard announcing The Book of Why, by Judea Pearl and Dana Mackenzie, a book to be published in May 2018 by Basic Books. This book confronts the hoary old adage, "Correlation is not causation," which has been taught to generations of statisticians and scientists and used as a pretext to avoid talking about causation. Pearl has developed mathematical algorithms for reasoning about cause and effect, and the book gives numerous examples of how these can be put into practice. It is intended for a popular (non-technical) audience.
G4G13
Dana Mackenzie
public
G13-100
Sam Loyd Puzzles You Have Not Seen
Puzzle
In 1909, the Lyon Manufacturing Co. of Brooklyn, NY, published a small advertising booklet for Mexican Mustang Liniment. The booklet contained sixteen Sam Loyd puzzles, most signed with Loyd’s name. Most of the puzzles were duplicates or redrawn designs of puzzles that appeared in either Sam Loyd’s Cyclopedia of Puzzles or his Sam Loyd's Puzzles: A Book for Children, and some appeared in later publications like Houdini's Red Magic Section, but three of the puzzles cannot be traced to these or other original sources. My exchange gift is a reproduction of these three puzzles. Note that I first learned about Sam Loyd as a sixth grader in 1972 after purchasing a paperback copy of The Scientific American Book of Mathematical Puzzles and Diversions by Martin Gardner.
G4G13
Michael Tanoff
public
G13-098
Puzzle Stickers
Puzzle
Art
My contribution to the gift exchange is stickers hiding clues leading to a mathematical treasure hunt I'm hosting across my blog and a few other spots on the internet. I also have a physical prize for the first person to reach the end.
G4G13
Dominika Vasilikova
public
G13-097
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
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
Does the Barber Shave Himself?
Puzzle
Word Play
Bookmark with philosophiocal logic puzzle.
G4G13
Delicia Kamins
public
G13-091
Urabe-Pattern
Art
I was surprised at M.C. Escher’s exhibition in 1982 and hoped to create a tiling pattern by myself. But I worried about creating everyday, and time was gone without any one pattern during 2 months. When I watched Escher’s sketch book, I found thinner additional line behind butterfly design. It gave me the inspiration to make section paper like top page. I invented 2 kinds section paper of square and triangle. I select segment line by “try & error” method. I could create 200 tiling patterns during one year.
At that time, I did not know that tiling pattern were infinite. Prof. Gisaku Nakamura’s book taught me that there were rotation method of square and triangle. He selected all tiling pattern from tetragon and polyiamond by programming. (I found some polyiamond leakage from his list). I also found the possibility to create the tiling pattern to adopt arc on straight line. I programmed all possibility of tiling pattern from his list and print them by plotter in 1985. Their total page was too big and total thickness of paper was 30 feet. Prof. Gisaku Nakamura taught me his tiling pattern of rotation element were infinite. Then I must give up to plotting out.
G4G13
Toshinaga Urabe
public
G13-090
Exploding Kittens - First Edition Game
Game
Exploding Kittens is a highly-strategic, kitty-powered version of Russian Roulette. Players draw cards until someone draws an Exploding Kitten, at which point they explode, they are dead, and they are out of the game. UNLESS that player has a Defuse card, which can defuse the kitten using things like laser pointers, belly rubs, and catnip sandwiches. All of the other cards in the deck are used to move, mitigate, or avoid the Exploding Kittens.
This special First Edition copy of the game is a collector's item and will never be printed again. We hope you love it as much as we do!
G4G13
Elan Lee
Jordan Gold
public
G13-089
The X-Y Chart
Rec Math
My gift exchange item is called an X-Y Chart. It is a very unique chart of multiplication facts for elementary school students. My friend, Joe Speier, who was concerned about children learning their multiplication facts designed the chart. During a visit with Martin, I shared it with him along with some of Joe's interesting ideas about how children learn multiplication.
Joe Speier
G4G13
Charles Sonenshein
public
G13-088
Global Maps - Past and Future
Art
Science
Two Lenticular cards from Germany - one shows Pangea the last supercontinent 300 million years ago, and the second card shows the map of the globe in the next Heat Age when all the ice melts. This may result in a net gain in land!
G4G13
Timothy Rowett
public
G13-087
Multimodular Origami: A Truncated Icosahedron
Art
Rec Math
This document contains original diagrams and instructions for making a truncated icosahedron (Buckyball) using hexagon and hexagon/pentagon strip modules designed by the author.
G4G13
Thomas Cooper
public
G13-085
13 Sided and Suits Dice
Game
Toy
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
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
untitled (Tangle toy)
Puzzle
Toy
G4G Give-away
G4G13
NA NA
public
G13-080
Transparent Sheets
Art
Magic
Two transparency sheets chosen at random from a larger selection. Combining any two different sheets reveals a different secret image. Exchange recipients are encouraged to find each other and combine sheets to reveal all of the images.
G4G13
Andrea Hawksley
Andy Lutomirski
public
G13-078
Spixel Puzzle
Art
On the picture you can see the visual design of my Gift Exchange item. The object is based on aligning RGB Spidron puzzles.
G4G13
Dániel Erdély
public
G13-077
A Figurative Tree
Art
Artwork of a low-resolution figurative tree.
G4G13
Robert Bosch
public
G13-075