Gathering 4 Gardner 8
Speakers, titles, and abstracts
As of 24 March 2008
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Speaker |
Presentation |
(Tentative) Schedule |
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Scott Aaronson Massachusetts Institute of Technology |
The Limits of Quantum Computers In the popular imagination, quantum computers would be almost magical devices, able to "solve impossible problems in an instant" by trying exponentially many solutions in parallel. In this talk, I'll describe several results in quantum computing theory, due to myself and others, that directly challenge this view. So for example, we now know that, at least in the "black-box model" that we know how to analyze, quantum computers would need exponential time to break cryptographic hash functions or find local optima, just as classical computers would. I'll also describe how one can sometimes "turn lemons into lemonade," and use the limitations of quantum computers to create new quantum learning algorithms. |
Sunday PM |
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Adam Atkinson
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Applications of Vampires in Law and Medicine Given what we know about vampires from shows such as Buffy and Ultraviolet, various ways they could be used to solve legal and medical problems spring to mind. |
Sunday AM |
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Tom Banchoff Brown University |
Slicing (Hyper)Cubes in "Flatland: the Movie" Slices from the new animation "Flatland: the Movie" recall sections of Martin Gardner's four-dimensional columns, challenging new generations of students and teachers. Look for 4 x 8. |
Thursday AM |
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Lowell W. Beineke Purdue University |
Loyd's Courier Problem: Pythagoras, Diophantus, and Martin Gardner In Sam Loyd's Courier Problem, an army fifty miles long is marching at a constant speed. A courier, also going at a constant speed, rides from the rear of the army to the front and back again, returning at exactly the time when the army has advanced its length, fifty miles. The problem is to determine how far the courier travels. In a second version, the army has a square formation, fifty miles on a side, and the courier goes all the way around the army, again returning just when the army has advanced its length. In both versions, the answer is an irrational number. We present some work of Owen O'Shea on versions of the puzzle for which the answer is an integer. |
Saturday PM |
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George Bell Boulder, CO |
The shortest game of Chinese Checkers and related puzzles In one of his Scientific American columns, Martin Gardner introduced several puzzles originating from the game of Chinese Checkers (now a chapter in his book: Penrose Tiles to Trapdoor Ciphers). In 1971, Octave Levenspiel considered how quickly a single player could move their pieces from one side of the board to the other, and found a solution in 27 moves. We employ computational search to show that this is the shortest possible such crossing. David Fabian found a complete game of two-person Chinese Checkers in 15 moves by each player, we show that no shorter game is possible. |
Sunday AM |
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George Bohigian St. Louis, MO |
An Ancient Eye Test-Using the 8 Stars of the Big Dipper Vision testing in ancient times was as important as it is today. The predominant vision testing in some cultures was the recognition and identification of constellations and celestial bodies of the night sky. A common ancient naked eye test used the double star of the 8 stars of the Big Dipper in the constellation Ursa Major or the Big Bear. The second star from the end of the handle of the Big Dipper is an optical double star. The ability to perceive this separation of these two stars, Mizar and Alcor, was considered a test of good vision and was called the "test' or presently the Arab Eye Test. This presentation is the first report of the correlation of this ancient eye test to the 20/20 line in the current Snellen visual acuity test. This presentation describes the astronomy, origin, history and the practicality of this test and how it correlates with the present day Snellen visual acuity test. |
Thursday PM |
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Robert Bosch Oberlin College |
Recent Progress in Opt Art We will describe recent progress in using mathematical optimization techniques to create pictures, portraits, and sculpture. Examples will include Domino Artwork, TSP Art, and Edge-Constrained Tile Mosaics. |
Saturday PM |
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Kenneth Brecher Boston University |
A Torque About Tops
Spinning tops have delighted and intrigued people for at least three
thousand years. By seeming to defy gravity while pointing towards a
fixed direction in space or precessing around it, they offer puzzlers
and magicians as well as mathematicians and physicists, much food for
thought. In this presentation, I will give a brief overview of the
history of tops as both toys and scientific tools. I will also
demonstrate the motion of several kinds of tops with unusual
properties, ending with the counter-intuitive motion of rattlebacks
made of wood, glass, pewter and other materials. |
Thursday PM |
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Vladimir Bulatov Corvallis, OR |
Making Organic Geometrical Sculpture I will show and explain process of creating organic sculptures based on various geometrical ideas using custom interactive software and rapid prototyping technologies. |
Thursday PM |
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Wyatt Casey
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Promoting Math Education through Math Magic
Math magic can be used to engage students into mathematical studies and
activities. It can intrigue, inspire, and empower children at the
elementary level on up. I have performed voluntary classroom magic for
the last five years. Much of what I do has been inspired by the
writings of Martin Gardner. In particular, his book “Mathematics Magic
and Mystery” has provided me with a wealth of tricks and an inspiration
to promote mathematics education through Math Magic. I would like to
present four math magic tricks that I use to primarily intrigue
students: |
Saturday PM |
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Harold Cataquet Cataquet & Associates |
Presenting the Knight's Tour An overview of the knight's tour as a feat of mental and/or mathematical acumen. The talk will also discuss the most recent findings in the analyses of the knight's tours. |
Sunday AM |
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Martin Chlond University of Central Lancashire |
OR MAGIC:Mathematics, Art and Games in the Classroom The session will promote the use of interesting and unusual applications of OR modeling techniques taken from the literature of recreational mathematics. The purpose is to encourage the use of such offbeat examples to capture the attention of students and stimulate motivation to learn. |
Thursday PM |
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Barry Cipra Northfield, MN |
Sudokuniqueness The speaker will describe a sneaky ploy that can come in handy solving certain difficult sudokus. |
Saturday PM |
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John Conway Princeton University |
(TBA)
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Thursday AM |
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Bill Cutler Bill Cutler Puzzles, Inc |
A New Puzzle Program A computer program has been written to solve 2-d packing problems in which the pieces and box are irregular shapes. The program has been successful in solving most of Edi Nagata's puzzles. |
Saturday AM |
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Wayne Daniel Genoa, NV |
178 Saw Cuts & Some Glue Steps taken to construct a puzzle with the shape of the Icosahedron/Dodecahedron Dual. The 'talk' will be a video. |
Thursday AM |
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Frans de Vreugd Katwijk, The Netherlands |
Puzzle Locks from India
India has a rich history in making padlocks with special tricks to open
them. On a trip to India we visited Hiren Shah, who has a magnificent
collection of over 500 of these (mostly antique) puzzle locks. In this
talk I will show many of the wonderful mechanisms of these locks from
his collection in full detail. |
Friday AM |
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Erik Demaine Massachusetts Institute of Technology |
Hinged Dissections Do every two polygons of the same area have a hinged dissection, that is, a hinged chain of pieces that can be folded into either polygon? This problem goes back implicitly to 1902 and has been studied extensively in the past ten years, culminating in a complete solution only this year. It turns out that the answer is yes, even if the goal is to fold into several different polygons. Furthermore, the hingings can be folded continuously without self-intersection, and the number of pieces is somewhat reasonable. Our result (joint with Timothy Abbott, Zachary Abel, David Charlton, Martin Demaine, and Scott Kominers) generalizes and builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our result to edge-hinged dissections of solid 3D polyhedra that have an (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. All of our proofs are constructive with algorithms to compute the hinged dissections and motions between configurations. Hinged dissections have possible applications to reconfigurable robots, programmable matter, and nanomanufacturing. |
Thursday AM |
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Stewart Dickson Beckman Institute, Univ. Ill. at Urbana-Champaign |
Vedic Geometry and Tactile Mathematics In the Hindu Vedic texts, there is contained a unified system of doing mental arithmetic. Most of these techniques can be taught in Elementary School. However, as intuitive as Vedic Mathematics is, it is also almost purely symbolic and abstract, having little connection or concern for Geometry. The practice of creating Digital, Mathematical sculpture reveals that the abstract description of form becomes separated from the form when it is rendered physical -- a breakdown in communication of Modernist Abstract sculpture. The speaker proposes self-describing mathematical sculpture and asks whether Vedic Mathematics can lead to an intuitive description of functions describing three-dimensional surfaces. |
Sunday PM |
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Michael Ecker Pennsylvania State University Wilkes-Barre Campus (Lehman, PA) |
A Survey of Fun Paradoxes Paradoxes - How can you pass your body through a postcard? Can a surface really hold a finite volume of paint but not be painted (infinite surface area)? How does this last example (Gabriel's horn) relate to fractals, the von Koch snowflake, Star Trek's warp drive, and the human intestines? We will also consider wordplay with logical paradoxes, such as those that are offshoots of Russell's paradox. More frivolous: What's the deal with time travel? How can removing balls from an urn lead to no balls or infinitely many? (This is a more fun version of Zeno's paradox that I owe to Underwood Dudley.) |
(TBA) |
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Stanley Eigen Northeastern University |
The 2008 IG Nobels A summary of the recent Ig Nobel winners and some video from the prize ceremony. |
Saturday AM |
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Yossi Elran Weizmann Institute of Science, Rechovot, Israel |
A Graeco-Latin Search Game Martin Gardner was intrigued by Graeco-Latin Squares and dedicated a chapter in one of his books to the subject (Euler Spoilers). The beauty of Graeco-Latin squares and their practical use in experiment design has been known for decades. In our talk, we will present a new puzzle based on both Graeco-Latin squares and the well-known word search puzzles. The mathematical aspects of the game will be discussed, as well as possible generalities and specific puzzles concerning the theme of G4G8 (eight, infinity). |
Thursday PM |
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Michele Emmer University of Rome |
The Adventure of the Square The adventure of the square in the land of modern art until the vitory. |
Friday AM |
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Daniel Erdely Spidron bt. |
Spidron's oddities I am going to present some of our surprising new findings, which encourage us to continue our long-term investigation of the movement and other interesting properties of Spidrons . We undertook here to present the peculiar tilting of some of the spidron edges during the continuous spidron movement, spidronized Penrose-tilings, the Kepler-tile shadows of certain edges of quasicrystals that are defined by the bisections of them by specific spidron-nests, and other curiosities. |
Sunday PM |
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Dick Esterle nobbly wobbly |
8 ways to Sunday and the AMAZING geometry Machine A spinning figure 8 creates two spheres and it's lazy cousin on its side dance toward the spherical counterparts of the Platonic Solids counting from 1 to 6. The Amazing Geometry MAchine continues to stick to its loops. |
Thursday PM |
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Jeremiah Farrell Indianapolis, IN |
Word Ways A discussion of the 41 year old Journal started by Martin Gardner (Word Ways: Journal of Recreational Linguistics) |
Thursday AM |
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Robert Fathauer Tessellations, Phoenix, AZ |
The Art of Fractal Knots A widely-applicable method for iterating knots is described. This method relies on substitution of portions of a knot with smaller copies of the entire knot. A starting knot is first arranged as a patch of tiles that contains individuals tiles similar in shape to the overall patch. Iterative substitution leads to the creation of complex knots that are often esthetically pleasing, particularly for knots possessing a high degree of symmetry. The iteration process is designed to allow repetition ad infinitum; i.e., an infinite number of iterations leads to a fractal knot that is in many cases unicursal. |
Saturday PM |
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David Finkelstein Georgia Institute of Technology |
Decoding Dürer Dürer's engraving MELENCOLIA I has puzzled many viewers since 1514. It exists in two states with significant differences, and has dozens of unreported subliminal images and encipherments. It uses symbols all found in the Bible, the Hieroglyphica of Horapollo (already used by Dürer in the same year), and the Occult Philosophy of Agrippa (derided by Dürer, perhaps for Agrippa's astrology). Together these indicate a double message. Both messages are encapsulated in an anagrammatical legend that is now the name of the engraving. A rebus in Dürer's coat-of-arms for the word caelo, meaning both "I engrave" and "at heaven", helps to unscramble the anagram. The overt message, which has already been read by Panofsky, is that absolute truth and beauty are inaccessible to the artist/scientist, causing the melancholy of the legend. The covert message, however, is that Natural Philosophy, Gateway I to Heaven, is superior to Mathematical and Theological Philosophy. The innocuous admission of the limitations of science veils a manifesto of the impending scientific revolution that would otherwise have been a capital offense. |
Sunday PM |
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Greg Frederickson Purdue University |
Unfolding an 8-high Square, and Other New Wrinkles A geometric dissection is a cutting of a geometric figure into pieces that we can rearrange to form another geometric figure. In this talk, I will focus on hinging the pieces with a "piano hinge", which connects two pieces along a shared edge and allows a folding motion. I will dissect and then fold a figure that is p levels thick to a second figure that is q levels thick, where q is not equal to p and all pieces are connected into one assemblage by piano hinges. Characteristic of such dissections, and apropos for G4G8, is a 12-piece folding dissection of an 8-high square to a 1-high square. Besides squares, I will also deal with Greek crosses, Latin Crosses, Crosses of Lorraine, regular hexagons and stars. Looking for folding dissections with the fewest number of pieces makes this activity more challenging. And for some dissections, just identifying an appropriate sequence of folds is not so easy. I will demonstrate some of these folding dissections with video and others with computer animation. |
Thursday PM |
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Jordan Goldklang "Jordini" Mill Valley, Indiana University |
Majoring in the Magic of Performance I am majoring in Magic at Indiana University through the Independent Major Program. I have been working with horn professor (and fellow magician) Jeff Nelson on the art of performance. I will be speaking about my past experience of performing through magic and also as a violinist, and what it takes to give a great performance. |
Sunday AM |
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Jan Grashuis Arabesk |
Arabesk: the educational project Arabesk is a non-profit organization that promotes puzzles, games and objects related to physics, mathematics and logic. Amongst many other activities we developed (under the name Brainpleasers, in dutch: Breinkwekers) a package of two boxes containing 25 games and puzzles each for primary schools. In relation to these packages workshops are offered to introduce the teams of primary schools how to work with this kind of (addional) educational materials. These workshops are given by a school supporting organization. The content and philosophy will be elaborated on in the talk. |
Sunday AM |
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George Hart Stony Brook University |
Screw-Together Puzzles Various people have designed geometric assembly puzzles in which the parts screw together in a surprising way. I will survey the ones I know and present some new ones of my own design, including my gift exchange item. |
Thursday PM |
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Robert Henderson and Harry Nelson Mason, MI |
Solving Harry Nelson's Pohaku Slide Puzzle Challenge Describes methods used to improve the shortest solution for Harry Nelson's IPP27 Pohaku slide puzzle challenge from 189 moves to the minimal 49 moves, winning the challenge prize of $151. |
Sunday PM |
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Jim Henle Smith College |
The Proof and the Pudding I am writing a book about mathematics and gastronomy. The two subjects don't interact. I don't apply mathematics to cooking. And I don't apply cooking to mathematics. Instead, I present the two fields side-by-side to show some essential similarities and also to make a few points about creativity, taste, problem-solving, philosophy, modern society, aesthetics, and the pursuit of pleasure. The talk will be about this project. |
Sunday AM |
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Akio Hizume Star cage institute of Geometry |
Inter-Native Architecture of Music I will talk about the music and architecture based on the Golden Mean. I will also talk about what I built in Tom's garden as mathematical heritage. |
(TBA) |
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Haruo Hosoya Ochanomizu University (Emeritus) |
Discovery of Interesting Properties of 4000-Year Old Pythagorean Triples.
Systematic Classification and Construction |
Thursday AM |
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Thomas Hull Merrimack College |
The Puzzle-Nature of Modular Origami Modular (or Unit) Origami involves folding multiple pieces of paper into identical shapes that can lock together, without glue, to form polyhedral shapes. Once the units are folded, the task of locking them together to make a desired shape is identical to that of a puzzler trying to reassemble a polyhedron dissection puzzle. There is also a strong parallel between the design of modular origami models and that of polyhedron dissection puzzles. In this talk I will illustrate these parallels, describe the process of modular origami design, and highlight some of the mathematical symmetries it can capture. |
Thursday AM |
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Ray Hyman Professor Emeritus of Psychology, University of Oregon |
A Magic Square Routine A demonstration of a magic square where the magic total corresponds to the age of a relative merely thought of by a volunteer. I have gathered ideas from many sources to devise a square that requires a minimum of memory and mathematical ability. A volunteer secretly writes the name and age of relative. The performer quickly fills in the sixteen cells of a 4x4 matrix with numbers. When the volunteer reveals the age of her relative, the performer reveals that the relative's age equals the totals for each row, column and many other combinations of 4 cells of the square. As an added revelation, the performer asks the volunteer the name of her relative. The performer turns over the pad on which the square has been written to reveal that the relatives name is printed on the back. |
Sunday PM |
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Glenn Iba Lexington, MA |
Explorations of dynamic tiling (inspired by the game of Tetris) The video game Tetris can be viewed as an example of "dynamic tiling", where a rectangular space is filled with various shapes (tetrominos), but since completed (horizontal) rows are cleared, the tiling has a dynamic nature. In particular, gaps can later potentially be filled by clearing space to "uncover" the gap, and then fill it. I have developed a puzzle variant of Tetris, implemented as an interactive software game called "Target Tiling", that uses these ideas. The key ideas are: (1) to tile an exact rectangle using the dynamic row-clearing rule, (2) to define a clear objective (clearing all rows, or equivalently, dynamically tiling a rectangular space), and (3) making the piece sequence deterministic so that solving is feasible. The implemented game simulator is quite general (allowing 3-D rectangular space; 3-D pieces of varying sizes; variations of piece set; and changing parameters such as board width, height, & depth). The result is a very interesting space of challenges, and a rich domain for mathematical exploration. |
Saturday PM |
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Hirokazu Iwasawa Yokohama, Japan |
Tricky Solutions for Integrals with Crazy Lazy Eight Some improper integrals can be evaluated in some elementary but very tricky ways. I show several examples of such tricky solutions. And I invite you to enjoy what I call "Definite Integral Puzzle" as recreation. |
Friday AM |
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Slavik Jablan The Mathematical Institute, Serbia |
Knot Theory- Some Open Problems We will consider several open problems: uknotting (unlinking) number, unlinking gap, knots and links with unknotting number one, invertibility, amphicheirality, undetectability, non-algebraic tangles and polyhedral links. |
Friday AM |
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Harold Jacobs North Hollywood, CA |
Euclid in Color One of the most eccentric mathematics books of all time was Oliver Byrne's edition of Euclid's Elements. Published in 1847, it is also one of the most beautiful. This talk will present the story of this wonderful book. |
Thursday PM |
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Kate Jones Pasadena, MD - publisher of Martin Gardner's games |
Philosophy revisited: 8 great memes Martin Gardner's first interest and the field in which he has his degree was Philosophy. This important part of his life is often obscured by math, magic and puzzles. His book, "The Whys of a Philosophyical Scrivener," discusses all the -isms he isn't, and what he has finally chosen to be. Likewise, I shall enumerate 8 fundamental insights drawn from all those areas, including the games and puzzles I've designed, inspired by Martin's work. At G4G7 I had presented 7 principles and promised David Singmaster to supply 8 for G4G8. Here they are. |
Sunday PM |
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David C. Kelly Hampshire College Summer Studies in Mathematics |
Problems from and Problems with the Interesting Test Since 1971 the Interesting Test (new each year) has been used to select exceptionally strong high school students for the Hampshire College Summer Studies in Mathematics. The IT, like the program, is designed to promote engagement with and enjoyment of the processes of mathematical thinking, not simply with the results of that thought. This talk will present some of the IT problems, puzzles, sources, and activities that have worked well and a few that flopped. |
Saturday AM |
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Tanya Khovanova Massachusetts Institute of Technology |
Number Gossip Have you ever heard of evil numbers? How about odious numbers? I will tell you what they are. What is the largest amount of coin money you can have without being able to make change for a dollar? You can bring your answer to this talk. What is so special about 1210? You will learn that too. You will be able to find out many things about your favorite numbers. |
Saturday PM |
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Ken Knowlton Budd Lake, NJ |
Geometric strategies for "Knowlton" mosaic tilings Underlying mosaics, one of the oldest of art forms, lies the matter of partitioning space into areas - one such area for each item ("terresa"). I have used well-known methods, such as "large pixels" but also nonce (subject-specific, once only) methods, especially for my mathematician and puzzle minded colleagues, each of whom has inadvertantly suplied the idea. Several slides will illustrate my methods and observations. |
Saturday AM |
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Jerzy (Jurek) Kocik Southern Illinois University |
Looking through the Apollonian Window The whole world seems to reflect itself in the Apollonian window — a special fractal design of circles. One can find there Pythagorean triples, intriguing integer recurrence sequences, pieces of sacred geometry (including Golden Ratio, Vesica Pisces, and pi), and puzzle-like rearrangements of circles with surprising properties. And even traces of Dirac scissors trick. |
Saturday PM |
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Yoshiyuki Kotani Tokyo University of Agriculture and Technology |
The same puzzles which are seemingly different We sometimes find a puzzle is completely equivalent or similar in logic or mathematics to another puzzle. We sometimes transform some puzzle to totally different one in shape. There are such pairs of puzzles in all types, which are mathematical, logical, mechanical, or of their combination. They have the same logical internal structure, which can be enjoyed to study. I show a few pair of such puzzles, some are my original ones, and some are well known. There are four topics: (1)Batting order problems of baseball, (2) Square Filling Puzzles, (3) Sliding Puzzles and Ring Puzzles, and (4) A Digit Filling Puzzle. |
(TBA) |
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Lee Krasnow Pacific Puzzleworks (Oakland, California) |
Recent Advancements in Rhombic Dodecahedral Puzzle Analysis Software Exciting new advancements have been made in the field of interlocking puzzle analysis software! During this presentation, I will give the audience a brief overview of Andreas Röver's open source "BurrTools" puzzle analysis software, including demonstrations of how it may be used to solve rectilinear burr puzzles, and also how it may be used to help design new ones. From there, I will discuss how this software has been extended to work with non-rectilinear geometric dissections such as triangular prisms, spheres, and now (finally!) the Right-Angle-Tetrahedron joins the list. The addition of this new geometry space allows analysis of a wide range of "Stewart Coffin" style puzzles which are based on dissections of the rhombic dodecahedron. After discussing some of the considerations made (and problems encountered) as this new functionality was developed, I will demonstrate how to model and solve many of the R-D puzzles written about in Stewart Coffin's "Puzzling World of Polyhedral Dissections". Q&A to follow. |
Sunday PM |
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Peter Lamont University of Edinburgh |
The Rise of the Indian Rope Trick The Indian Rope Trick was, for many years, the best-known secular miracle in the world. It remains the greatest legend of the East, and one of the most famous illusions in the history of magic. According to historians, it is of ancient origin, the feat was observed by Marco Polo and, in 1875, a vast reward was offered by the Viceroy of India for a single performance. Magicians searched in India for the secret and claimed they had found it, and countless ordinary witnesses claimed to have seen it. But the legendary feat has never been performed, and the legend comes from neither the ancient past nor India. So how and where did the legend begin, how did a never-performed feat become so famous, and what did the witnesses see? In this talk, Dr Peter Lamont reveals the truth behind one of the world's most extraordinary myths. |
(TBA) |
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Mogens Larsen Department of Math. Sciences, Univ. of Copenhagen |
Physical Mathematics I present a sample of application of physical thoughts in proving mathematical theorems in a different way than the usual Euclidean standard. |
Sunday AM |
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Shannon Lieb Butler University |
Soap Bubbles and Local Hidden Variables?
Interest in spherical, colored bubbles has long caught the interest of
the young and old alike. Soap bubbles are the common source of
these amusing and ephemeral objects. Mathematicians, scientists
and engineers (among others) are passionate in their desire to take the
common everyday observations and abstract from them generalizations
that can be applied to seemingly unrelated areas of knowledge.
The general phenomenon of a tension existing in the surface of a drop
of liquid and its manifestations, have applications that range from
recent attempts to understand the nature of the atomic nucleus to the
theories of the genesis of our planetary system [Ref 1]. Balloons
as models of soap bubbles: In an attempt to explain the ideal gas law
(PV=nRT) for closed, isothermal systems, teachers will use a balloon as
an example of how to visualize the effect of increasing the pressure
inside the balloon by increasing the exterior pressure on the balloon
(i.e., squeezing the balloon with their hands) and then predicting the
effect on the volume of gas. Because of the use of the balloon as
an idealized boundary between the enclosed gas and the surroundings,
one ignores the fact that the balloon surface is far from ideal (as is
also the case for a soap bubble). The following proposed
experiment can be performed with either soap bubbles or balloons with
the same results. Attach two equivalent balloons to a connecting
valve (three way stopcock for instance) and inflate them to two
different sizes. Then allow the two balloons to be connected to
one another through the valve so that they can exchange their
contents. First, anticipate the results of this experiment.
Include in your anticipated results an explanation based on your
(educational) experience and/or common sense. Now do the
experiment! |
Saturday AM |
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Roger Malina Leonardo Organisation |
Mathematics Made Flesh: Art, Scientific Simulation and A Life The Leonardo organisation was founded in 1968 to promote interaction between contemporary artists with scientists and engineers. The first project was the publishing of the scholarly Leonardo Journal, now part of the Leonardo Publishing program with the Leonardo Book Series at MIT Press. Over 40 years more than 5500 artists and researchers have documented their work in the Leonardo projects (http://www.leonardo.info). From the early algorithmic artists to todays artists using genetic algorithms, scientific simulations and artificial life, mathematical and computer artists laid the foundations for digital media and interactive games. Today as new branches of mathematics develop, such as in network theory, artists rapidly incorporate new mathematical ideas into their work and sometimes make significant contributions to mathematical knowledge in the process. |
Saturday AM |
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Scot Morris
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Amazing Eight Scot extends his scrutiny of numerology, "the one true pseudoscience." |
Friday AM |
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David P Moulton Center for Communications Research |
Averaging Points Two at a Time
In 2006 Brendan McKay asked the following on sci.math.research: We have
n points in a disk centered at the centroid of the points. We
successively replace the two furthest points from each other by two
copies of their average. (After each move we still have n points with
the same centroid.) How many moves are necessary to guarantee that all
points lie in the concentric disk of half the radius? |
Thursday AM |
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"Card Colm" Mulcahy Spelman College, Atlanta |
Genetic Evolution - One to Eight Inclusive We explore some card tricks based on new discoveries involving special arrangements of the numbers 1 to 8 inclusive. |
(TBA) |
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Ted Nelson Oxford Internet Institute |
A New Agenda for Mathematics Math teaching today is pessimized for discouragement and disaffection. Ask most people and they will say they hated mathematics, along with history. Now this is particularly strange. Consider history. History can be learned in any order. Yet they spoil it. And guess what? Math too can be learned in any order. What's that you say? We've tried different curricula? You're not hearing me. The problem is HAVING a curriculum-- a fixed sequcnce and schedule for all students. Students are consumers, whether you like it or not. If we want to entice them, they must be given great choice and variety-- instead of the grind of fixed sequence, we must give them the fun of shopping. (Shopping, it should be noted, is research.) I propose, instead of a curriculum, a cafeterium. We tell the students what they must know and offer them different pathways to get there. (What they should know is a juicy question separate from this proposal.) Of course this must be testable. But we need minimal testable modules, connected in as many ways as possible. We want to show the crystalline beauties of the mathematical universe much earlier than is presently allowed. What's that you say? This can't fit in today's educational system? It's the system that doesn't fit. The system doesn't fit the subject and it certainly doesn't fit the students. |
Saturday PM |
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Bruce Oberg Sucker Punch Productions |
I H8 8 Wherein the prosecution makes its case. |
Friday AM |
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Adrian Ocneanu Penn State |
Shadows of four dimensions and a mechanical quaternion machine We present several constructions, large scale sculptures and movies on four dimensional regular structures and of their movements. We present a large scale quaternion machine which uses 25 cogwheels to convert interactively these sculptures into symmetries. |
(TBA) |
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Tohru Ogawa The Interdisciplinary Institute of Science,Technology and Art & University of Tsukuba |
A New Type of Transformation from 4D to 3D and Some 3D Designs A New Type of Transformation from 4D to 3D and Some 3D Designs including a family of space curves and "Ms Donut" (A Torus-related design) and some other interesting motions. |
Thursday PM |
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Chris Palmer University of Colorado at Boulder |
SlideTab Surface Creation System
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Sunday PM |
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Jean Pedersen Santa Clara University |
Stop-Sign Theorems The Star of David Theorems, involving six binomial coefficients are well-known. In this talk we will discuss a way to arrive at the generalized Star of Daivid Theorems and then discuss some new Stop-Sign theorems involving eight binomial coeffieicnts. |
Saturday AM |
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Ed Pegg Jr.
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Meet the Attendees An Introduction Machine! |
Friday AM |
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Sebastien Perez-Duarte Frankfurt, Germany |
Conformal mappings and photography Conformal mappings are an 19th century area of mathematics, and their application to cartography goes back to those heroic times. Unknowingly (or not) they are also the subject of many drawings by M.C. Escher, and recent work has shown the connection to conformal mappings. I will show how these techniques can be applied to photography, both traditional and spherical, to produce interesting results. |
Saturday AM |
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Jim Propp University of Massachusetts Lowell |
Pi over 8, by way of infinity I'll demonstrate a simple mathematical contraption that uses rotating arrows and moving chips to compute better and better approximations to pi over 8, generating an interesting 4-colored picture in the process. |
Sunday AM |
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Rinus Roelofs Hengelo, the Netherlands |
Single Surface Structures Normally structures of interwoven layers are built with two or more surfaces. In my talk I will show and explain structures of interwoven layers built with only layer. |
Sunday AM |
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Karl Schaffer De Anza College/Dr. Schaffer and Mr. Stern Dance Ensemble |
Imaginary Dances Mathematical descriptions of a swirling movement pattern popular in many forms of dance often make use of the quaternions. In this interactive presentation t |