Abstract

Symmetry: Culture and Science
Volume 37, Number 3, pages 245-246 (2026)
https://doi.org/10.26830/symmetry_2026_3_245

SYMMETRY ACROSS BORDERS

Simone Brasili, Johan Gielis

Dear Readers,
Symmetry has always crossed borders. As Hermann Weyl emphasized, its roots lie deeply in mathematics, yet it also appears in natural forms, biological structures, architecture, art, education, and in the ways different cultures interpret order, balance, transformation, repetition, and invariance.

For this reason, symmetry should not remain isolated within abstraction. Its mathematical foundations provide precision and generality, but its broader significance emerges when abstract structures encounter concrete phenomena, educational practices, artistic forms, scientific questions, and cultural traditions. Crossing disciplinary borders does not weaken mathematics. Rather, it creates new contexts in which mathematical ideas can be interpreted, applied, and discussed.

A central aim of Symmetry: Culture and Science is precisely to provide a meeting place for mathematics, science, the humanities, the arts, architecture, and education. Symmetry can act as a common language among these fields without erasing their differences. Concepts such as invariance, transformation, proportion, repetition, balance, and asymmetry can be approached from distinct perspectives and compared across disciplines.

The papers in this issue offer a clear example of this crossing of borders. The first article, by Ángel Colín, connects geometry, visualisation, artistic construction and learning. Symmetry becomes a concrete educational resource through which students develop spatial sense and geometric thinking.

Sergey V. Petoukhov and Vitaly I. Svirin explore connections among mathematics, biology, genetics, and algebraic modelling, considering relationships between phyllotaxis, Fibonacci structures, genetic coding, and biological symmetries.

Petar Mladinić and Nikol Radović bring mathematics into dialogue with natural form. Through geometric transformations and dynamic geometry, floral structures become objects of mathematical visualisation and investigation.

Finally, Bramasta Putra Redyantanu and Stephanus Wirawan Dharmatanna connect symmetry with architecture, landscape, climate, and spatial experience. Particularly suggestive is the idea of the threshold: a border that not only separates spaces but also becomes a place of transition and encounter.

This image of the threshold also expresses the spirit of the present issue. Borders can divide, but they can also become spaces of exchange.

The same perspective looks forward to the Symmetry Festival 2027 in Tokyo, where scholars from different countries and disciplines will meet and where symmetry will enter into dialogue with the Japanese tradition of Katachi. This encounter will provide a concrete opportunity for exchange between Eastern and Western traditions of thinking about form, structure, meaning, and transformation.

The papers collected here already anticipate this direction. From mathematics education to biology, from floral forms to tropical architecture, symmetry appears where different fields, methods, and cultures meet.

Perhaps this is one of its most enduring strengths: symmetry allows us to recognise relationships without erasing differences. Symmetry Across Borders is therefore an invitation to continue creating spaces where abstraction meets experience, science meets culture, and different traditions of thought can encounter one another.

We invite you to follow updates on the Katachi website, https://katachi-jp.com and on our journal website, https://journal-scs.symmetry.hu, and, as we prepare for this international event.

Save the date: 9-12 August 2027, Tokyo, Japan.