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.
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
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
for all nonnegative integers i, j such that j ≤ i, as illustrated in Figure 1.1. The points in R2 associated...
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
There are several improvements for bipartite network ﬂows . 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...
A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY
&BURDICK ),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.