G4G13

Motley Cube

Scott Kim

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.

G13-002

G4G13

Tensegritiy Pop-up

Robert Connelly

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.

G13-003

G4G13

1 to 8 Squared

Jaap Scherphuis

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

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G4G13

12...N Polygons for Plane Tiling

Yoshiyuki Kotani

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.

G13-019

G4G13

Laser Cut Pythagorean Theorem Puzzle

Gerard Westendorp

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.

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G4G13

Spectrominoes

Ron Taylor

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.

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G4G13

G4G13 Logo Design

Vandorn Hinnant

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.

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G4G13

A Fair Die of 13 Faces

Ryuhei Uehara

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.

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G4G13

G4G13 Latin Square Puzzles

David Nacin

Puzzle

Rec Math

A small collection of Latin square themed puzzles created in honor of the G4G13 conference.

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G4G13

Postcard and Tiny Piece of Equilateral Tridecagon Tiling

Masaka Iwai

Art

Rec Math

I prepared postcards and tiny pieces of "Equilateral Tridecagon Tiling" for the Gift Exchange.

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G4G13

Cause to Wonder

Lina Menna

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.

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G4G13

How Safe Is It?

Barney Sperlin

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!

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G4G13

G4G13 Clock Face

Skona Brittain

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.

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I plan to submit a paper containing a photo of nine $100 bills and your task will be to cut them up and rearrange the pieces to make ten $100 bills. I also will include a copy of the Vanishing Leprechauns, as they appeared in Gotcha! In addition to the paper for the exchange, I also will bring copies of the money paradox for you to cut up.]]>

G4G13

Money From Nothing: Or Why the Serial Number Now Appears Twice on Each Piece of Currency

Stuart Moskowitz

Puzzle

Rec Math

Martin Gardner introduced me to Vanishing Area Paradox Puzzles in Aha! Gotcha! with the Vanishing Leprechaun Puzzle. He explained the paradox by describing an old counterfeiting method. I've learned the method and so I'm going to share it with you. But before you get too excited, you should know that the government has now learned how to thwart this method of making money from nothing, thus the title of the gift. Does that make this gift worthless?

I plan to submit a paper containing a photo of nine $100 bills and your task will be to cut them up and rearrange the pieces to make ten $100 bills. I also will include a copy of the Vanishing Leprechauns, as they appeared in Gotcha! In addition to the paper for the exchange, I also will bring copies of the money paradox for you to cut up.

I plan to submit a paper containing a photo of nine $100 bills and your task will be to cut them up and rearrange the pieces to make ten $100 bills. I also will include a copy of the Vanishing Leprechauns, as they appeared in Gotcha! In addition to the paper for the exchange, I also will bring copies of the money paradox for you to cut up.

G13-059

G4G13

Nontransitive Dice for Three Players

James Grime

Rec Math

With nontransitive dice you can always pick a dice with a better chance of winning than your opponent. There are well known sets of three or sets of four nontransitive dice. Here we explore designing a set of nontransitive dice that allows the player to beat two opponents at the same time. Three player games have been designed before using seven dice. We introduce an improved three player game using five dice, exploiting a reversing property of some nontransitive dice.

G13-060

G4G13

Mental Factoring Cheat Sheet

Richard Schroeppel

Hilarie Orman

Rec Math

This is a summary of mental factoring, the essential information condensed into two pages.

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G4G13

PiTop

Kenneth Brecher

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.

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G4G13

Poly-Twostors Periodic Table, Catalog of 3D Printer Models

Akio Hizume

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.

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G4G13

13 Serpentine Symmetries

Susan Goldstine

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.

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G4G13

Multimodular Origami: A Truncated Icosahedron

Thomas Cooper

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.

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G4G13

The X-Y Chart

Joe Speier

Charles Sonenshein

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.

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G4G13

A Gift of the Number 13 for G4G13

Joe DeVincentis

Rec Math

Science

Participants will receive one spruce cone along with instructions on how to read the number 13 in it.

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