Abstract

Symmetry: Culture and Science
Volume 36, Number 3, pages 229-230 (2025)
https://doi.org/10.26830/symmetry_2025_3_229

REVISITING MATHEMATICS TO SOCIETY THROUGH THE APPLICATIONS OF SYMMETRY

Simone Brasili, Johan Gielis

Dear Readers,

We are pleased to introduce the third issue of SCS journal, which is directly linked to the previous volume, Symmetry in Contexts: From Mathematics to Society where symmetry is considered as a bridge between abstract principles and real-world applications across disciplines.

The volume is structured into two parts. The first part draws on classical mathematical frameworks to generate new insights into symmetry and structure. The second part presents extended versions of select abstracts originally featured at the Symmetry Festival in Pisa offering a rich array of interdisciplinary applications of symmetry in society, including manufacturing, information, and music. The first two papers in this issue share a common root: they are derived from Pythagorean concepts, reflecting the influence of ancient mathematical thought in contemporary studies of symmetry.

Luděk Spíchal’s article constructs a lemniscate-like curve grounded in the Pythagorean means (arithmetic, geometric, harmonic). These curves, while visually reminiscent of the lemniscate of Bernoulli, offer new algebraic behaviours and symmetrical properties that enrich the field of mathematical visualization.

Toni and Koya Chehlarova contribute a second Pythagorean-themed piece, presenting an interactive representation of the Pythagorean Tree using dynamic animations accessed through embedded QR codes.

Their work exemplifies the power of technology in visual learning and offers an innovative model for engaging students in STEAM education.

Andréia Hall’s article continues in the mathematical domain. However, she shifts the focus toward pedagogy, exploring how professional development courses for teachers utilize artistic media and craft-based symmetry (e.g., quilting, ceramics) to deepen mathematical understanding and creativity. This paper exemplifies how symmetry education can effectively bridge the gap between art and mathematics across various educational levels.

In the second part of the issue, Alessio Pacini, Francesco Lupi, and Michele Lanzetta explore asymmetry in manufacturing as both a design challenge and an opportunity. Through a systematic literature review, they demonstrate how asymmetry can be viewed not as an imperfection but as an intentional feature that enhances performance and functionality in engineering systems.

After that, Matteo Tonoli and Massimo Bustreo introduce a novel conceptual framework, “Diattology,” which combines design theory, cybernetics, and information science. They propose a worldview by subtraction, emphasizing informational density and minimalism as the hallmarks of good design. Referencing principles from Apollonian harmony and Italian postwar design, they present symmetry as a measure of communicative efficiency.

Ultimately, in the field of music, Konstantin Zenkin examines periodicity and cyclic recurrence as fundamental expressions of symmetry in musical composition. His article crosses generations and traditions to highlight how symmetrical structures influence musical time, emotion, and narrative.

Altogether, this issue showcases symmetry not just as a geometric or mathematical feature, but as a transversal principle that connects logic, creativity, design, culture, and information. Whether derived from ancient means or modern digital tools, symmetry continues to be a beautiful language for interpreting and shaping our world.

We thank all our contributors and readers for their support of this ongoing journey through the many applications of symmetry from mathematics to society and beyond.