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The aim of this paper is to obtain a classification of scrolls of genus 0 and 1, which are defined by a one-dimensional family of lines meeting a certain set of linear spaces in ${\bf P}^n$. These ruled surfaces will be called incidence…
This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt…
We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…
Sports are a popular and effective way to illustrate physics principles. Baseball in particular presents a number of opportunities to motivate student interest and teach concepts. Several articles have appeared in this journal on this…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
The aim of this note is to give a formula expressing the trace form associated with the 27 lines of a cubic surface.
This is an exercise based approach to matrix groups. The idea is to collect a bunch of exercises at one place which anyone with basic knowledge of linear algebra can attempt to solve and learn matrix groups and algebraic groups.
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the…
We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…
We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Given a smooth curve $\gamma$ in some $m$-dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat…