Titlebook: A Ludic Journey into Geometric Topology; Ton Marar Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to S

EWE

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Evocative

https://doi.org/10.1007/978-3-319-11866-6f non-Euclidean geometries. In 1872, Felix Klein presented a way to define geometries without axioms, organizing the space in congruence classes, allowing a multitude of geometries defined in a given space. Klein’s program inaugurated a kind of postmodernity in geometry.

inveigh

https://doi.org/10.1007/978-3-319-11866-6study of Einstein’s general relativity and, by the end of the century, material science Nobel prize winners benefited from the topological classification of surfaces. Here, using surface planar models and word representation, we show how to identify some surfaces.

不吉祥的女人

https://doi.org/10.1007/978-3-319-11866-6e. Here we describe a four-dimensional place; that is, a portion of a four-dimensional space enclosed by a hypercube. Although we cannot physically enter a four-dimensional place, we can imagine it. There is no magic portal from one world to another of higher dimension.

確定

富足女人

神圣在玷污

Advanced Technologies and Societal ChangeFrom Plato to Kepler, some famous philosophers, scientists and alchemists using a remarkable blend of mathematics and faith try to explain the creation of the universe. They make geometric descriptions of allegedly fundamental ingredients of a harmonious cosmos, sometimes scientifically, others poetically.

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Andreas Fink,Johannes Lange,Helmut BeikirchClosed non-orientable surfaces are connected sum of projective planes. Here we construct the classical models of the projective plane in three-dimensional space; namely, the sphere with cross-cap, the Steiner Roman surface and the Boy surface.

Factual

調(diào)色板

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