Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Point–line–plane postulate"'
Autor:
Rolf Struve
Publikováno v:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 59:221-246
The principle of duality is well established in projective geometry but can hardly be found in the literature on Euclidean geometry where it is “more a principle of analogy than a scientific principle with a logical foundation” (cp. Sommerville,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a18eccc12cc4fd8db8307cb3262aa715
https://doi.org/10.1007/s13366-017-0370-6
https://doi.org/10.1007/s13366-017-0370-6
Autor:
Rolf Struve
Publikováno v:
Journal of Geometry. 107:707-717
In Euclidean geometry and in absolute geometry fragments of the principle of duality hold. Bachmann (Aufbau der Geometrie aus dem Spiegelungsbegriff, 1973, §3.9) posed the problem to find a general theorem which describes the extent of an allowed du
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a8774f5a70d66074ce4d2af7a708266b
https://doi.org/10.1007/s00022-016-0314-6
https://doi.org/10.1007/s00022-016-0314-6
Publikováno v:
Journal of Automated Reasoning
Journal of Automated Reasoning, Springer Verlag, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
Journal of Automated Reasoning, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
Journal of Automated Reasoning, Springer Verlag, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
Journal of Automated Reasoning, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
online first; International audience; In this paper we focus on the formalization of the proofs of equivalence between different versions of Euclid's 5 th postulate. Our study is performed in the context of Tarski's neutral geometry, or equivalently
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5295cfedebbea0e5f43a1d51340f29ca
https://hal.inria.fr/hal-01178236v2/document
https://hal.inria.fr/hal-01178236v2/document
Autor:
Rolf Struve
Publikováno v:
Journal of Geometry. 107:225-248
We present a common axiomatic characterization of Cayley-Klein geometries over fields of characteristic \({\neq 2}\). To this end the axiom system of Bachmann (Aufbau der Geometrie aus dem Spiegelungsbegriff, 2nd edn. Springer, Heidelberg 1973) for p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::52bd07c9c561afef7237bed68e2cf184
https://doi.org/10.1007/s00022-015-0293-z
https://doi.org/10.1007/s00022-015-0293-z
Autor:
Zalman Usiskin
Publikováno v:
Advances in STEM Education ISBN: 9783319614335
Almost 50 years ago, Arthur Coxford and I developed a high school geometry course in which geometric transformations were fundamental to the mathematical development. Properties of reflections and size changes (dilations) were taken as postulates and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0c02afb88a2c33eadc0912f7483191fe
https://doi.org/10.1007/978-3-319-61434-2_12
https://doi.org/10.1007/978-3-319-61434-2_12
Autor:
Boris Čulina
Publikováno v:
Axiomathes.
In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the homogeneity of spac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ca8e3db12b76508f2da3c8062523b01f
https://doi.org/10.1007/s10516-017-9358-y
https://doi.org/10.1007/s10516-017-9358-y
Autor:
Toshikazu Sunada
Publikováno v:
Progress of Theoretical Physics Supplement. 116:235-250
The aim of this note is to give a survey of recent studies on spectral geometry. In the course of discussion, we put an emphasis on relationships between discrete group actions and the spectra of the Laplacian and magnetic Schrodinger operators on a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5d8749b4db2c45b43556c445d1e14a8
https://doi.org/10.1143/ptp.116.235
https://doi.org/10.1143/ptp.116.235
Autor:
Ryan Hoban
Publikováno v:
The College Mathematics Journal. 44:126-134
SummaryMany classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersectio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a508ef90354a0954368b143f77742bfd
https://doi.org/10.4169/college.math.j.44.2.126
https://doi.org/10.4169/college.math.j.44.2.126
Publikováno v:
International Mathematical Forum. 8:1185-1193
A set A in Euclidean n-space En, is called an m-convex set if for every m distinct points of A at least one of the line segments joining two points of them lies in A. In this article we study some geometrical and topological properties of these sets
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::699bc599d3cd3403ac3efeab4d3e82e1
https://doi.org/10.12988/imf.2013.3354
https://doi.org/10.12988/imf.2013.3354
Publikováno v:
Elemente der Mathematik. 68:96-114
We study the geometry of a Euclidean triangle from a Mobius geometric point of view. It turns out that its in- and ex-centers can be constructed in a symmetric and Mobius invariant way. We relate this construction to Thurston's center of symmetry of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b422c3eb4186e79d3e307fdbfff70c06
https://doi.org/10.4171/em/228
https://doi.org/10.4171/em/228