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Hyperbolic geometry is a type of non-Euclidean geometry that arose historically when mathematicians tried to simplify the axioms of Euclidean geometry, and instead discovered unexpectedly that changing one of the axioms to its negation actually produced a consistent theory.
Hace 4 días · In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.
Hace 1 día · In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
Hace 1 día · A Riemannian metric makes it possible to define many geometric notions, including angles, lengths of curves, areas of surfaces, higher-dimensional analogues of area ( volumes, etc.), extrinsic curvature of submanifolds, and the intrinsic curvature of the manifold itself.
Hace 5 días · Our study also offers atlas options for constructing more sophisticated hierarchical networks and explains the association between key brain regions and NDD. Conclusion: MHNet leverages multi-view feature learning from both Euclidean and non-Euclidean spaces, incorporating high-order information from BFNs to enhance NDD classification performance.
Hace 4 días · Not until Lobachevsky (1829) and Janos Bolyai (1832) had published their ideas of non-Euclidean geometry – for the first time in the history of mathematics – Gauss himself put down his ideas, but avoided any influence to the contemporary scientific discussion, because he did not publish about it.
Hace 5 días · in parallel with the teaching of Euclidean geometry, on topics of non-Euclidean geometry in the formative itineraries of the New High School (NEM). oT do this, we searched the literature for theoretical foundations on these topics, applications in ariousv disciplines
