In order to improve the advantages and the reliability of the second derivative method in tracking the position of extrema from experimental curves, we develop a novel analysis method based on the mathematical concept of curvature. We derive the formulas for the curvature in one and two dimensions and demonstrate their applicability to simulated and experimental angle-resolved photoemission spe...

The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise mathematical definition exists. In this paper, we adopt an axiomatic approach to the problem, and attempt to produce a satisfactory measure.

Through a case study of a series of Galton Board activities, we try to offer some reflections about the possibility of integrating in the teaching model different tools, starting from completely physical activities and arriving through gradual steps of abstraction to the “virtualization” of the tools and to the corresponding abstraction of underlying mathematical concepts.

The marriage of art and mathematics has been widespread and productive, but almost nowhere more productive than in the world of origami. In this paper I will discuss how mathematical ideas led to the development of powerful tools for origami design and will present a step-by-step illustration of the design and realization of a representational origami figure using mathematical design algorithms...

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving investigation and discovery activities. This paper presen...

Increasingly, companies are taking part in process improvement programmes, which brings about a growing need for employees to interpret and act on data representations. We have carried out case studies in a range of companies to identify the existence and need of what we call Techno-mathematical Literacies (TmL): functional mathematical knowledge mediated by tools and grounded in the context of...

Mathematical constructions and concepts can be utilized in a number of methods to investigate the process of generating architectural forms. One is to technically layout architectural elements along such constructions, another is to explicitly develop forms corresponding exactly to the underlying concept, and another is to use such concepts as inspiration, a starting point for design. A hybrid ...

Simple random walk and Brownian motion are two strongly interconnected mathematical concepts. They are widely involved in not only pure math, but also in many other scientific fields. In this paper I will first introduce and define some basic concepts of discrete-time random walk. Then I will construct Brownian Motion with some basic properties, and use a method called the strong approximation ...

As a domain of application and reference for the proposed approach, we focused on Constructionism, a theory that studies the use of technology in the creation of educational environments. The most well known pragmatic result of Constructionism is the Logo programming language which, for the past 20 years, has been used by millions of students as a fertile soil for the development of critical re...