Although the lines of constant coordinate values in curvilinear coordinates may not always be straight lines, it may still be that they intersect at right angles. See, for example, the diagram for 2-D polar coordinates, Fig. 6.2. Here the lines of constant r, though circles, cross the line...
Specifically, it is more adapted to drawing curves or circles than an X-Y device might be able to, like we saw with this similar sand-drawing plotter. Also, if allowed to rotate its entire 360-degree reach instead of just the 90 degrees shown in the video, a machine like this could ...
What was peculiar to Des Cartes, however, was the speculative interest which made it impossible for him to rest in mere experience, whether of things spiritual or things secular, which made him search, both in our consciousness of God and our consciousness of the world, for the links by whi...
For a generic choice of the diffusivities, we shall prove that patterns emerge in the Cartesian product provided they can develop in at least one of the two networks from which the Cartesian support originates. In this respect, Cartesian products are more prone to exhibit Turing instabilities ...
product of lower-order invariants and can thus be eliminated for redundancy. In other words, a valid combination illustrated in Fig.1i needs to correspond to one connected graph, rather than two disconnect graphs of lower body orders. For instance, terms such as\({B}_{i,cn012}^{(4)}=...
determination of the coordinates of any point in space according to well-defined operational procedures. In this way we avoid all undefined geometrical primitives, such as the points, lines and circles of Euclidean geometry. The following definitions endow vectors with the usual properties ...
The virtual-pictorial level allows dynamic color changes of the virtual images (such as circles or squares in a diligent manner) but without allowing for the virtual movement of these images from one place on the screen to another. The virtual-abstract level allows for the dynamic manipulation ...