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Theodore Xenophon Barber (1927–2005) was an American psychologist who researched and wrote on the subject of hypnosis, [1] publishing over 200 articles and eight books on that and related topics.
She decided to make more durable models, and did so by crocheting them. [4] The first night after first seeing the paper model at the workshop she began experimenting with algorithms for a crocheting pattern, after visualising hyperbolic planes as exponential growth. The following fall, Taimiņa was scheduled to teach a geometry class at Cornell.
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which points are represented by points on the forward sheet S + of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space or by the displacement vectors from the origin to those points, and m ...
There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disk model, the Poincaré half-plane model, and the Lorentz or hyperboloid model. These models define a hyperbolic plane which satisfies the axioms of a hyperbolic geometry. Despite their names, the first three mentioned above were introduced as models ...
The metric of the model on the half-plane, { , >}, is: = + ()where s measures the length along a (possibly curved) line. The straight lines in the hyperbolic plane (geodesics for this metric tensor, i.e., curves which minimize the distance) are represented in this model by circular arcs perpendicular to the x-axis (half-circles whose centers are on the x-axis) and straight vertical rays ...
The order 7-3 rhombic tiling shown in a portion of the band model. The band model is a conformal model of the hyperbolic plane. The band model employs a portion of the Euclidean plane between two parallel lines. [1] Distance is preserved along one line through the middle of the band.
In the Poincaré half-plane model one convenient choice is the portion of the half-plane with y ≥ 1. [7] Then the covering map is periodic in the x direction of period 2 π , and takes the horocycles y = c to the meridians of the pseudosphere and the vertical geodesics x = c to the tractrices that generate the pseudosphere.
The hyperbolic growth of the world population and quadratic-hyperbolic growth of the world GDP observed till the 1970s have been correlated by him and his colleagues to a non-linear second order positive feedback between the demographic growth and technological development that can be spelled out as follows: technological growth – increase in ...
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