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Funding Information: Aalto Math&Arts visit to Shanghai was funded by Dean Tuomas Auvinen from School of Arts, Design and Architecture, Dean Jouko Lampinen from School of Science and Dean Gary Marquis from School of Engineering. The collaborators in Shanghai were West Bund Art Center, Sino-Finnish Centre, students and teachers from Tongji-Huangpu School of Design & Innovation and teachers from other schools in Shanghai, Beijing and other provinces of China as well as students from Tongji University. Funding Information: Mathematics and Arts Colloquium in connection with a multidisciplinary course like this is a well-functioning concept. Public talks related to ongoing new activities at the university provide an accessible and convenient channel for a broad audience. Art gives a fruitful frame to make mathematics more visible in the society. The Colloquium was supported by Niilo Helander Foundation. Publisher Copyright: Copyright © 2021 The Korean Association for Radiation Protection. Aalto University has been able to create a fruitful frame for activities enhancing interaction between mathematics, art and architecture. One of the most recent highlights of this progress was a student exhibition titled ‘IN TRANSITION – Mathematics and Art’ [12] at Espoo Cultural Centre [9]. The exhibition was further extended to the Aalto Math&Arts exhibition in Shanghai ([3],[25]). In this paper we describe our long-lasting open-minded collaboration to build a minor in Mathematics and Arts that is useful from freshmen to PhD students across the conventional barriers between disciplines. A dialogue between scientific and artistic practices break clichés related to mathematics by bringing deep phenomena in the field to the level of human experience. Challenges and future scenarios are discussed broadly. Some ideas about the present state of Aalto Math and Arts can be found in [2].

The purpose of the article is to present the evolution of the use of mathematical language as an inspiration for creating spatial, three-dimensional forms in art and architecture. The article focuses on the possibilities for art and architectural design ideas gained by contemporary mathematics, algorithms and computational parametric approach. The analysis of various examples represents the relationships between the composition of spatial forms and the rules of mathematics. It is evident in different time frames, different styles and different approaches to thinking about and creating art and architecture. The starting point for this analysis is the symbolic Vitruvian golden ratio and its impact on the principles of spatial forms composition. Next, using the study of the geometric art of folding and cutting paper to create three-dimensional spaces, elements of applied art or even furniture or clothing, the article reaches to the mathematical issue of fractals, as the most accurate illustration of the aims of the parameterization in contemporary architecture. Parametric architecture, as a way of thinking about building as a set of numerically coded aspects, demonstrates the possibilities of using mathematical resources to improve functioning of the building by using optimization algorithms. The article shows possibilities of such uses of mathematics in generating spatial forms. Further, this analysis asks about the possible risks and disadvantages of such an approach, wondering if the correct definition of architecture is possible to achieve simply by using language of mathematics without all the other immeasurable aspects.

This paper presents an approach for representing space-filling curves by sound, aiming to add a new way of perceiving their beautiful properties. In contrast to previous approaches, the representation is such that geometric similarity transformations between parts of the curve carry over to auditory similarity transformations between parts of the sound track. This allows us to sonify space-filling curves, in some cases in up to at least five dimensions, in such a way that some of their geometric properties can be heard. The results direct attention to the question whether space-filling curves exhibit a structure that is similar to music. I show how previous findings on the power spectrum of pitch fluctuations in music suggest that the answer depends on the number of dimensions of the space-filling curve.

This paper presents an approach for representing space-filling curves by sound, aiming to add a new way of perceiving their beautiful properties. In contrast to previous approaches, the representation is such that geometric similarity transformations between parts of the curve carry over to auditory similarity transformations between parts of the sound track. This allows us to sonify space-filling curves, in some cases in up to at least five dimensions, in such a way that some of their geometric properties can be heard. The results direct attention to the question whether space-filling curves exhibit a structure that is similar to music. I show how previous findings on the power spectrum of pitch fluctuations in music suggest that the answer depends on the number of dimensions of the space-filling curve.

Design grammars as one of the well-known generative design formalisms have evolved and been tested for nearly 40 years across a wide range of design disciplines including architectural design, product design, engineering design and so on. Over the years, grammar research has transformed from the early focus of mathematical models to the current computational implementations. This paper revisits the grammatical approach to generative design, and presents the conceptual framework of Generative Design Grammars (GDG) together with a demonstration for supporting dynamic and autonomous design in contemporary CAAD tools i.e. 3D virtual environments. Integrated with an agent model and a simulation engine, GDG provides an intelligent approach towards dynamic and autonomous design. This intelligent approach to utilising computer technologies in design implies both opportunities and challenges for designers.

Since at least the time of the Ancient Greeks, scholars have argued about whether the golden section—a number approximately equal to 0.618—holds the key to the secret of beauty. Empirical investigations of the aesthetic properties of the golden section date back to the very origins of scientific psychology itself, the first studies being conducted by Fechner in the 1860s. In this paper historical and contemporary issues are reviewed with regard to the alleged aesthetic properties of the golden section. In the introductory section the most important mathematical occurrences of the golden section are described. As well, brief reference is made to research on natural occurrences of the golden section, and to ancient and medieval knowledge and application of the golden section, primarily in art and architecture. Two major sections then discuss and critically examine empirical studies of the putative aesthetic properties of the golden section dating from the mid-19th century up to the 1950s, and the empirical work of the last three decades, respectively. It is concluded that there seems to be, in fact, real psychological effects associated with the golden section, but that they are relatively sensitive to careless methodological practices.

In this paper, the teaching of mathematics, the arts and architecture are presented as tools for outreach and learning of Mathematics. Three key components are addressed: First, the various activities performed by the mathematicians and mathematics teachers are presented in terms of the conceptual, the applied and the pedagogical. Second, it focuses on applied Mathematics and Mathematics connections with other areas and, finally, the beauty of works of art from the point of view of Mathematics. For this, we present a variety of examples that relate to Mathematics and Art. En este artículo se presentan la didáctica de la matemática, las artes y la arquitectura como herramientas útiles en la divulgación y aprendizaje de la matemática. Se han abortado tres componentes fundamentales: la primera, presenta las diversas actividades que desempeñan los matemáticos y los docentes de matemática en cuanto a la parte conceptual, lo aplicado y lo pedagógico; la segunda, está enfocada hacia la matemática aplicada y vinculaciones de la matemática con otras áreas y, por último, la belleza de las obras de arte desde el punto de vista matemático. Para esto, se expone una gran variedad de ejemplos que vinculan la matemática y el arte.