Atomic solitons as a new class of solitons

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Atomic solitons as a new class of solitons - https://www.researchgate.net/publication/329455498_Atomic_solitons_as_a_new_class_of_solitons

 

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What is Hyperbolic Geometry?

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 Hyperbolic geometry is a type of non-Euclidean geometry that differs from classical Euclidean geometry in its treatment of parallel lines. In Euclidean geometry, parallel lines are equidistant and will never meet. In hyperbolic geometry, parallel lines can get arbitrarily close but will never intersect. Hyperbolic geometry is characterized by a constant negative curvature, meaning that lines curve away from each other, and objects in hyperbolic space appear to be "slimmer" than in Euclidean space. This leads to counterintuitive results, such as the fact that in hyperbolic geometry, there are more parallel lines to a given line through a point than there are in Euclidean geometry. Hyperbolic geometry has important applications in many areas of mathematics, including number theory, cryptography, and the study of Riemann surfaces. It is also used in physics to model the behavior of certain physical systems, such as the geometry of space-time in general relativity.
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Detail the Pythagorean influence on Plato's philosophy here.

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Pythagorean thought profoundly shaped Plato's philosophy, particularly in the realms of metaphysics, cosmology, and education: 1. **Theory of Forms**: The Pythagoreans believed that numbers were the fundamental principles of reality. Plato extended this idea into his Theory of Forms, where abstract, immutable entities (Forms) exist beyond sensory perception. Mathematical truths, which are independent of the physical world, exemplify the perfection and permanence of these Forms. 2. **Cosmology**: In *Timaeus*, Plato describes the universe as an ordered, geometric entity, reflecting Pythagorean ideas of mathematical harmony. He explains that the Demiurge (divine craftsman) structured the cosmos using mathematical principles, including the Platonic solids, emphasizing numerical ratios as the foundation of cosmic balance. 3. **Education**: Plato's emphasis on mathematical training as a path to philosophical enlightenment stems from Pythagorean thought. In *The Republic*, he outline...
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Islamic Aesthetics - Prof. Nasr

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