Related papers: Math and Dance: Notes from emerging interaction
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
The study of decimal numbers in secondary education is often approached from algorithmic perspectives, which limits students' understanding of their structure. This paper presents the task Footprints of the Walking of Numbers, a dynamic…
The enterprise of trying to explain different social and economic phenomena using concepts and ideas drawn from physics has a long history. Statistical mechanics, in particular, has been often seen as most likely to provide the means to…
Musical gestures connect the symbolic layer of the score to the physical layer of sound. I focus here on the mathematical theory of musical gestures, and I propose its generalization to include braids and knots. In this way, it is possible…
Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…
Choreographies are global descriptions of interactions among concurrent components, most notably used in the settings of verification and synthesis of correct-by-construction software. They require a top-down approach: programmers first…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
In this articles we consider very mathematical (if not very plausible) geometric marching. Our marchers will exhibit beautiful mathematics, some familiar and some less so. In a final summary section we discuss the point of all the fancy…
Ten short years ago, we had the rare privilege of witnessing the onset of a renaissance in science: humanity finally succeeded in its arduous quest to directly detect gravitational waves. This breakthrough did not occur in a vacuum: it was…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
The Web Geometry Laboratory, (WGL), is a blended-learning, collaborative and adaptive, Web environment for geometry. It integrates a well known dynamic geometry system. In a collaborative session, exchange of geometrical and textual…
Classroom discourse is a core medium of instruction - analyzing it can provide a window into teaching and learning as well as driving the development of new tools for improving instruction. We introduce the largest dataset of mathematics…
This paper explores the concept of engagement, the process by which individuals in an interaction start, maintain and end their perceived connection to one another. The paper reports on one aspect of engagement among human interactors--the…
Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other…
Generating full-body and multi-genre dance sequences from given music is a challenging task, due to the limitations of existing datasets and the inherent complexity of the fine-grained hand motion and dance genres. To address these…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative…
Since the 1960s a growing number of composers have engaged with scientific research and have tried to incorporate their understanding of various models and theories into their musical works. Among them, H\`ector Parra (b. 1976) has been…