In this paper we propose a new method, based on R-C similar transformation method, to study classification for the magic squares of order 5. The R-C similar transformation is defined by exchanging ...two rows and related two columns of a magic square. Many new results for classification of the magic squares of order 5 are obtained by the R-C similar transformation method. Relationships between basic forms and R-C similar magic squares are discussed. We also propose a so called GMV (generating magic vector) class set method for classification of magic squares of order 5, presenting 42 categories in total.
A simple parameterization of 3×3 magic squares Trenkler, Götz; Schmidt, Karsten; Trenkler, Dietrich
International journal of mathematical education in science and technology,
1/15/2012, Letnik:
43, Številka:
1
Journal Article
Recenzirano
In this article a new parameterization of magic squares of order three is presented. This parameterization permits an easy computation of their inverses, eigenvalues, eigenvectors and adjoints. Some ...attention is paid to the Luoshu, one of the oldest magic squares.
Discovery Neville de Mestre
Australian mathematics teacher,
01/2013, Letnik:
69, Številka:
3
Journal Article
Recenzirano
The following is the basis of an extension topic that I recently gave to mathematically- advanced Year 7 students at a local primary school. It could also be used for higher classes.
Polar and singular value decomposition of 3×3 magic squares Trenkler, Götz; Schmidt, Karsten; Trenkler, Dietrich
International journal of mathematical education in science and technology,
07/2013, Letnik:
44, Številka:
5
Journal Article
Recenzirano
In this note, we find polar as well as singular value decompositions of a 3×3 magic square, i.e. a 3×3 matrix M with real elements where each row, column and diagonal adds up to the magic sum s of ...the magic square.
This article summarises activities that happened during the first three weeks of a fictitious high-school-level linear algebra section that used magic squares as a teaching tool to inspire students ...to further investigate the topics. The author has been working with students from high school and college levels for years, and although this situation can be considered very realistic, it was not based on a single classroom, it is a product of imagination based on actual experience. This study focuses in the development of activities related to linear algebra with use of technology. An active learning method was used as the main strategy to motivate discovery. It aligns with the Australian Curriculum not only for the encouragement of using computers and calculators but also for helping the student understand the concepts and techniques in matrices and apply reasoning skills to solve problems with matrices, which are learning outcomes from Unit 2 Specialist Mathematics.
The definition of a regular magic square motivates us to introduce the new special magic squares, which are reflective magic squares, corner magic squares, and skew-regular magic squares. Combining ...the concepts of magic squares and linear algebra, we consider a magic square as a matrix and find the dimensions of the vector spaces of these magic squares under the standard addition and scalar multiplication of matrices by using the rank-nullity theorem.
In recent years, the approach of satisfiability modulo theories (SMT) has been very successful in solving many constraint satisfaction problems. In a typical SMT solver, the base constraints are ...expressed as a set of propositional clauses, where each Boolean variable is an abstraction of an atomic formula of first-order logic and the interpretation of the formula is constrained by a background theory. A widely studied theory is the linear pseudo-Boolean logic. Following this approach, we present an experiment of a SMT solver where the background theory can be specified in propositional logic and implemented by a procedure. We chose such a procedural background theory because we found no better ways to attack a previously open problem in combinatorial design, i.e., the existence of diagonally ordered magic squares of all orders.
This article covers how the West African khatimulu (Islamic numerical tables) are presently applied and taught in Western Europe. First, an introduction to the khatim is followed by a presentation of ...the context of the West African Mandinka marabout. Then, all the crucial components used in the design of the khatim - from the choice of initial sacrifice, the size of the khatim, the principles of numerology, the personalization of the khatim, the use of possible metaphysical agents, to Koranic quotes and physical substances to enhance the effect - is described. Further, the methods of two interviewed marabouts based in Sweden are compared with the classic Islamic esoteric literature and earlier ethnographic research. Finally, the clients for the services of the marabouts based in Western Europe are identified as primarily non-Muslim native Europeans, not West Africans.
The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ...and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected.The Mathematics of Various Entertaining Subjectsbrings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics.
Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more.
Looking at a plethora of eclectic games and puzzles,The Mathematics of Various Entertaining Subjectsis sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.
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