Mathematical Recreations Research Articles

Beyond Swinging: Hinged Dissections that Twist or Fold

A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way on the hinges, and form the other figure when swung another way. In addition to using “swing hinges”, which allow rotation in the plane, we can use “twist hinges”, which allow one piece to be flipped over relative to another piece via rotation by 180° through a third dimension. Furthermore, we can use “fold hinges”, which allow rotation along a shared edge, a motion that is akin to folding. This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models. Bio: Greg N. Frederickson is a Professor of Computer Science at Purdue University, in West Lafayette, Indiana. His primary area of research is the design and analysis of algorithms, and he has served on the editorial boards of SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Algorithmica, and IEEE Transactions on Computers. He also pursues interests in mathematical recreations, specifically geometric dissection. On this topic he has published three books and a number of articles. He has twice won the George Polya Award from the Mathematical Association of America.

Notes on Contributors

Notes on Contributors

Hidden word

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Famous puzzles of great mathematicians

This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. The selected problems do not require advanced mathematics, making this book accessible to a variety of readers. Mathematical recreations offer a rich playground for both amateur and professional mathematicians. Believing that creative stimuli and aesthetic considerations are closely related, great mathematicians from ancient times to the present have always taken an interest in puzzles and diversions. The goal of this book is to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework. Concise biographies of many mathematicians mentioned in the text are also included. The majority of the mathematical problems presented in this book originated in number theory, graph theory, optimization, and probability. Others are based on combinatorial and chess problems, while still others are geometrical and arithmetical puzzles. This book is intended to be both entertaining as well as an introduction to various intriguing mathematical topics and ideas. Certainly, many stories and famous puzzles can be very useful to prepare classroom lectures, to inspire and amuse students, and to instill affection for mathematics.

Alan Turing's First Cryptology Textbook and Sinkov's Revision of it

Seventeen-year-old Alan Turing received a copy of the tenth edition of W. W. Rouse Ball's Mathematical Recreations and Essays as part of a school award. Ball's book contained a chapter titled “Cryptographs and Ciphers.” This might have been Turing's first cryptology textbook. In this paper we will examine what Turing could have found in Ball's chapter, and we will examine changes made to later editions by Ball and by Abraham Sinkov.

Maximizing the Probability of a Big Sweepstakes Win

Michael W. Ecker (DrMWEcker@aol.com) is an associate professor of mathematics at Pennsylvania State University's Wilkes-Barre Campus. He has taught college math since 1972, having received his Ph.D. in mathematics from the City University of New York in 1978 under the supervision of Harry Rauch. The founder of the AMATYC Review problem section in 1981, he has posed and solved hundreds of problems in over a dozen journals. He has also created several computer columns, including Mathematical Recreations in Byte and Recreational in both Popular Computing and Creative Computing. Since 1986 he has edited and published his own newsletter REC (Recreational & Educational Computing), featuring the unifying concept of Mathemagical Black Holes. He has written more than five hundred newsletters, columns, reviews, and articles, as well as five books and solution manuals. His other passions include racquetball, sweets, and new wife Renee.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

The IMS 2006 Quiz / Answers

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain teaser challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Brain Teaser Challenge

Various puzzles, humorous definitions, or mathematical recreations - usually having some relevance to electrical engineering - that should engage the interest of readers.

Using Dragon Curves to Learn about Length and Area

Art and Mathematics have often been combined to spark the imaginations of middle school students. “Dragon curves,” which are made with three tiles (see fig. 1), can be used to create fascinating patterns and to help students understand the concepts of length and area. Dragon curves have long been used in mathematical recreations. For example, Gale (1995) and Knuth and Knuth (1973) have written about art, games, and other activities that dragon curves can inspire. Dragon curves are generated by algorithms that create fractal images. The three tiles shown in figure 1 can be used to approximate these images.

Solutions to Calendar

Problems 1–24 and 30 were contributed by Victor G. Feser, University of Mary, 7500 University Drive, Bismarck, ND 58504-9652. Problem 25 appears in Madachy's Mathematical Recreations by JosephS. Madachy (New York: Dover Publications, 1979). Problems 26–29 were submitted by Larry Cusick and Agnes Tuska, both of California State University—Fresno, 5245 North Backer Avenue, Fresno, CA 93740.

Solutions to Calendar

Problems 1, 6, 26, and 27 were contributed by Harry Simon, 701 Viola Street, Eunice, LA 70535-4339. Problems 2, 7–11, 18, 19, 22, 25 and 31 were prepared by Bob Tex Kenney, P. 0. Box 454, Saipan, MP 96950. Problems 3, 4, 5, 21, and 23 were adapted from Mathematical Quickies by Charles W. Trigg (Mineola, NY: Dover Publications, 1985). Problems 12–14 and 20 were offered by Morris Jack DeLeon, Florida Atlantic University, Boca Raton, FL 33431. Problem 15 was submitted by Enrico Uva, Outreach Schools, 1741 de Biencourt, Montreal, PQ H4E 1T4. Problems 16, 17, and 24 were adapted from The Moscow Puzzles: 359 Mathematical Recreations by Bons A. Kordemsky (Mineola, NY: Dover Publications, 1992). Problems 29 and 30 were contributed by Mark Harbison, 5737 College Avenue, #23, San Diego, CA 92120.

The universe in a handkerchief: Lewis Carroll's mathematical recreations, games, puzzles, and word plays

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