Given a polygon A1, . . . , An, consider the chain of circles: S1 inscribed in the angle A1, S2 inscribed in the angle A2 and tangent to S1, S3 inscribed in the angle A3 and tangent to S2, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts t...

A common method for constructing blending Dupin cyclides for two cones having a common inscribed sphere of radius r > 0 involves three steps: (1) computing the (−r)-offsets of the cones so that they share a common vertex, (2) constructing a blending cyclide for the offset cones, and (3) computing the r-offset of the cyclide. Unfortunately, this process does not always work properly. Worse, for ...

We use the visualization and animation capabilities of Maple throughout our courses. Animations are used in presentations in class from first year onwards. For example, animations for Newton’s method and for fixed point iteration; to illustrate how slicing is used to generate the domain for double integration; to show how the error function (for the collocation method solution of a boundary val...

0. Introduction. With regard to the maximum principle, elliptic systems have been treated as a particular case of parabolic systems (see, for example, [W]). Therefore, the smallest set (that this approach can offer) which localizes pointwise the steady states is necessarily positively invariant with respect to the flow that the associated parabolic system induces. It turns out that one can do b...

The purpose of this work is to present simple time-optimal algorithms for a number of convexity-related problems on meshes with multiple broadcasting. More speciically, we show that with an n-vertex convex polygon P as input, the tasks of computing the perimeter , the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle shar...

We consider information flow via physical transport of inscribed media through space and compare it to information flow via electromagnetic radiation. Somewhat counterintuitively for point to point links, physical transport of inscribed mass is often energetically more efficient by many orders of magnitude than electromagnetic broadcast. And perhaps more surprising, even in a broadcast setting ...

Rectangle Packing is considered a difficult NP-problem which has several application areas such as integrated circuit systems, and pallet packing. Generally, Rectangle Packing Problems consist of a set of rectangles for which a configuration must be found, the intention is to minimise the surface-area of the configurations bounding box. Existing research has predominantly investigated algorithm...