In earlier work ([1]-[5]) the authors used the method of sweeping tangents to calculate area and arclength related to certain planar regions. This paper extends the method to determine volumes of solids. Specifically, take a region S in the upper half of the xy plane and allow the plane to sweep tangentially around a general cylinder with the x axis lying on the cylinder. The solid swept by S i...

The chromatic polynomials of ‘bracelets’ can be studied by means of a theory based on representations of the symmetric group. This paper contains a detailed study of the theory as it relates to one type of bracelet. The underlying theory is presented rather more clearly than hitherto, and some surprising features are exhibited. The methods involve an extension of the standard theory of distance...

The primary objective of this article is to explain about touch projector technology concept and how to use it. This paper intention is to look at the present touch projector as a new technology aimed to enable performing tasks as a huge touch screen. This paper briefs on the historical background and provide review of three recent devices which are Touch Pico, Cicret Bracelet and Dell Interact...

The chromatic polynomials of some families of quadrangulations of the torus can be found explicitly. The method, known as ‘bracelet theory’ is based on a decomposition in terms of representations of the symmetric group. The results are particularly appropriate for studying the limit curves of the chromatic roots of these families. In this paper these techniques are applied to a family of quadra...