Dalla Geometria Di Euclide Alla Geometria Dell'universo: Geometria Su Sfera, Cilindro, Cono, Pseudosfera - Convergenze (Paperback)
  • Dalla Geometria Di Euclide Alla Geometria Dell'universo: Geometria Su Sfera, Cilindro, Cono, Pseudosfera - Convergenze (Paperback)
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Dalla Geometria Di Euclide Alla Geometria Dell'universo: Geometria Su Sfera, Cilindro, Cono, Pseudosfera - Convergenze (Paperback)

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Paperback 198 Pages / Published: 31/08/2012
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Il testo confronta con la usuale geometria del piano (euclidea) vari tipi di geometrie che si hanno su superfici note e meno note: geometria sulla sfera, sul cilindro, sul cono e sulla pseudosfera. L'idea di fondo e di giungere alla descrizione "intrinseca" di queste geometrie analizzando che cosa significa l'andare diritto su queste superficie (cioe l'idea di geodetica). Si giunge cosi a vari tipi di geometrie che si discostano da quella euclidea usuale: geometrie localmente euclidee (su cilindro e cono deprivato del vertice), geometria ellittica (sulla sfera), geometria iperbolica (sulla pseudosfera). Si scopre che la chiave di volta concettuale che distingue queste diverse geometrie e la nozione di curvatura gaussiana, rispettivamente nulla su piani, cilindri, coni; (costante) positiva sulla sfera e (costante) negativa sulla pseudosfera. In relazione a queste idee matematiche si sviluppano anche vari temi interdisciplinari: si studiano ad esempio le caratteristiche delle carte geografiche che rappresentano la Terra a partire dal problema di determinare la rotta migliore tra due localita (porti, aereoporti); si indaga sulla curvatura del nostro universo; si descrivono le leggi geometriche su cui si basa la tecnologia dei GPS. Non si trascurano gli aspetti fondazionali, analizzando quali assiomi della Geometria Euclidea valgano o meno e perche nelle nuove geometrie.

Publisher: Springer Verlag
ISBN: 9788847025738
Number of pages: 198
Weight: 431 g
Dimensions: 234 x 157 x 10 mm
Edition: 2012 ed.


MEDIA REVIEWS

From the reviews: The authors describe elliptic (sphere), flat (cylinder, cone) and hyperbolic (pseudosphere) geometries, construct and study several projections and conformal mappings. The book can be recommended to everybody who teaches mathematics in high school, to students in mathematics, physics or engineering, to researchers in didactics of mathematics, especially of geometry, and to all those who want to understand that the Euclidean geometry is not enough to describe the universe. (Marian Ioan Munteanu, zbMATH, Vol. 1272, 2013)"


From the reviews:

The authors describe elliptic (sphere), flat (cylinder, cone) and hyperbolic (pseudosphere) geometries, construct and study several projections and conformal mappings. The book can be recommended to everybody who teaches mathematics in high school, to students in mathematics, physics or engineering, to researchers in didactics of mathematics, especially of geometry, and to all those who want to understand that the Euclidean geometry is not enough to describe the universe. (Marian Ioan Munteanu, zbMATH, Vol. 1272, 2013)"

From the reviews:

"The authors describe elliptic (sphere), flat (cylinder, cone) and hyperbolic (pseudosphere) geometries, construct and study several projections and conformal mappings. ... The book can be recommended to everybody who teaches mathematics in high school, to students in mathematics, physics or engineering, to researchers in didactics of mathematics, especially of geometry, and to all those who want to understand that the Euclidean geometry is not enough to describe the universe." (Marian Ioan Munteanu, zbMATH, Vol. 1272, 2013)

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