<abstract xmlns="http://www.w3.org/1999/xhtml">

The Spirograph is an old and popular toy that produces aesthetically pleasing and fascinating spiral figures. But are spirals all it can make? In playing with a software implementation of the toy, the author chanced upon a variety of shapes that it can make that are different from its well-known repertoire of spirals, in particular, shapes that have a visible flatness and not the curved spiral geometry that we are accustomed to seeing from the Spirograph. This paper reports on these explorations by the author and his delightful discovery of very elegant and simple geometric relationships between the Spirograph’s structural parameters that enable those patterns.
</abstract>

Flattening the Curve. . . of Spirographs

<abstract xmlns="http://www.w3.org/1999/xhtml">

Dots-and-Boxes is a popular children’s game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the same lattice game board structure as Dots-and-Boxes. The nature of these variations along with this lattice structure lends itself to applying Pick’s theorem to calculate claimed area. Several strategies similar to those studied in Dots-and-Boxes are used to analyze these new variations.
</abstract>

Dots-and-Polygons

<abstract xmlns="http://www.w3.org/1999/xhtml">

Arithmetic billiards show a nice interplay between arithmetics and geometry. The billiard table is a rectangle with integer side lengths. A pointwise ball moves with constant speed along segments making a 45° angle with the sides and bounces on these. In the classical setting, the ball is shooted from a corner and lands in a corner. We allow the ball to start at any point with integer distances from the sides: either the ball lands in a corner or the trajectory is periodic. The length of the path and of certain segments in the path are precisely (up to the factor √2 or 2√2) the least common multiple and the greatest common divisor of the side lengths.
</abstract>

Arithmetic Billiards

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we compare the efficiency of the decimal system to the efficiency of different mixed radix representations. We use as a starting point for our study the duodecimal systems suggested by Pascal and the Maya “Long Count” system. Using the quality index we experimentally show that two slight deviations from the duodecimal system are more efficient than the previous two systems and also than the decimal system.
</abstract>

Lagrange was Wrong, Pascal was Right

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three diferent factors. We conclude by classyfing the modes which are most musical according to our definition.
</abstract>

Musical Modes, their Associated Chords and their Musicality

AHEAD OF PRINT

Volume 11 (2024): Issue 18 (March 2024)

Volume 10 (2023): Issue 17 (January 2023)

Volume 9 (2022): Issue 16 (June 2022)

Volume 8 (2021): Issue 15 (November 2021)

Volume 8 (2021): Issue 14 (October 2021)

Volume 7 (2020): Issue 13 (November 2020)

Volume 6 (2019): Issue 12 (December 2019)

Volume 6 (2019): Issue 11 (September 2019)

Volume 5 (2018): Issue 10 (December 2018)

Volume 5 (2018): Issue 9 (September 2018)

Volume 4 (2017): Issue 8 (December 2017)

Volume 4 (2017): Issue 7 (May 2017)

Volume 3 (2016): Issue 6 (December 2016)

Volume 3 (2016): Issue 5 (March 2016)

Recreational Mathematics Magazine

The Recreational Mathematics Magazine is published by the Ludus Association with the support of the　Interuniversity Centre for the History of Science and Technology. The journal is electronic and semiannual, and focuses on results that provide amusing, witty but nonetheless original and scientifically profound mathematical nuggets. The issues are published in the exact moments of the equinox. It's a magazine for mathematicians, and other mathematics lovers, who enjoy imaginative ideas, non-standard approaches, and surprising procedures. Occasionally, some papers that do not require any mathematical background will be published.  Examples of topics to be adressed include: games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms, reviews and news.  Recreational mathematics focuses on insight, imagination and beauty. Historically, we know that some areas of mathematics are strongly linked to recreational mathematics - probability, graph theory, number theory, etc. Thus, recreational mathematics can also be very serious. Many professional mathematicians confessed that their love for math was gained when reading the articles by Martin Gardner in Scientific American.  While there are conferences related to the subject as the amazing Gathering for Gardner, and high-quality magazines that accept recreational papers as the American Mathematical Monthly, the number of initiatives related to this important subject is not large.  This context led us to launch this magazine. We will seek to provide a quality publication. We shall endeavor to be read with pleasure. In mathematics, the most important are the underlying ideas and nothing is as exciting as an amazing idea. So, we seek sophistication, imagination and awe.  Rejection Rate   50%   Recreational Mathematics Magazine is a journal for mathematicians who enjoy imaginative ideas, non-standard approaches, and surprising procedures. The journal addresses such topics as: games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group:   researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms  Financed by Fundação para a Ciência e a Tecnologia, I.P./MCTES through national funds (PIDDAC) – PTDC/HAR-HIS/28627/2017, UIDB/00286/2020 and UIDB/00678/2020. 