Euclidean plane

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  • This is a textbook on geometric algebra with applications to physics and serves also as an introduction to geometric algebra intended for research workers in physics who are interested in the study of this modern artefact. As it is extremely useful for all branches of physical science and very important for the new frontiers of physics, physicists are very much getting interested in this modern mathematical formalism.

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  • These lectures intend to give a self-contained exposure of some techniques for computing the evolution of plane curves. The motions of interest are the so-called motions by curvature. They mean that, at any instant, each point of the curve moves with a normal velocity equal to a function of the curvature at this point. This kind of evolution is of some interest in differential geometry, for instance in the problem of minimal surfaces.

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  • ON THE GROWTH RATE OF GENERALIZED FIBONACCI NUMBERS DONNIELL E. FISHKIND Received 1 May 2004 Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by summing along lines of slope t through the natural arrayal of Pascal’s triangle. We prove that √ α(t) 3+t is an even function. 1. Overview Pascal’s triangle may be arranged in the Euclidean plane by associating the binomial coefficient ij with the point 1 3 j − i, − i ∈ R2 2 2 √ (1.1) for all nonnegative integers i, j such that j ≤ i, as illustrated in Figure 1.1. The points in R2 associated...

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  • The publisher recently asked me to write an overview of the most common subjects in a first course of Calculus at university level. I have been very pleased by this request, although the task has been far from easy. Since most students already have their recommended textbook, I decided instead to write this contribution in a totally different style, not bothering too much with rigoristic assumptions and proofs. The purpose was to explain the main ideas and to give some warnings at places where students traditionally make errors....

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  • There are several improvements for bipartite network flows [2]. However they require the network to be unbalanced in order to substantially speed up the algorithms, i.e. either |U | |V | or |U | |V |, which is not the case in our context. The complexity of finding an optimal (minimum or maximum weight) matching might be reduced if the cost label is also a metric on the node set of the underlying graph. For example if the nodes of the graph are points in the plane and the cost label is the L1 (manhattan), L2 (Euclidean) or L∞ metric...

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  • A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY &BURDICK [1994]),which shares some of the features of these examples butwhich has a crucial difference as well. This example, likemany of the others, has the sym- metry group SE(2) of Euclidean motions of the plane but, now, the corresponding momentum is not conserved. However, the equation satisfied by the momentum associated with the symmetry is useful for understanding the dynamics of the prob- lem and how group motion can be generated.

    pdf41p loixinloi 08-05-2013 10 1   Download

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