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Euclidean Distance Geometry and Applications [PDF]
SIAM Review, 2014 Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances.
Leo Liberti +3 more
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Opportunity to Learn Euclidean Geometry in Two Mathematics Textbooks of Tenth Grade in South Africa
Edumatika, 2021 Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students.
Ugorji I. Ogbonnaya
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JOHME: Journal of Holistic Mathematics Education, 2022 The studies on the worked-out examples teaching approach (WOETA) have been investigated globally and in South Africa, showing gains in learners' performance. This study reports on the Euclidean geometry short learning programme (EGSLP), which used worked-
Msebenzi Rabaza, Joleen Hamilton
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Modeling 3D euclidean geometry [PDF]
IEEE Computer Graphics and Applications, 2003 This article compares five models of 3D Euclidean geometry-not theoretically, but by demonstrating how to implement a simple recursive ray tracer in each of them. It's meant as a tangible case study of the profitability of choosing an appropriate model, discussing the trade-offs between elegance and performance for this particular application.
Fontijne, D.H.F., Dorst, L.
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Minimal homogeneous submanifolds in euclidean spaces [PDF]
, 2002 We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally ...
Di Scala, Antonio Jose'
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On geometry on a two-dimensional plane in a five-dimensional pseudo-Euclidean space of index two [PDF]
E3S Web of ConferencesThe study of the geometry of surfaces having a codimension greater than one in multidimensional spaces is one of the most difficult problems in geometry. When the multidimensional geometry under consideration has a pseudo-Euclidean metric, its complexity
Mamadaliev Botirjon +2 more
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Making Euclidean geometry compulsory: Are we prepared?
Perspectives in Education, 2010 This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students.
Sonja van Putten +2 more
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A Pseudo-Euclidean Geometry [PDF]
Proceedings of the American Mathematical Society, 1959 The axioms to be used in this paper are, with only two exceptions, the same as those for abstract Euclidean vector spaces. We denote the elements by small letters and call them points. The null element 0, however, will not be considered a point. Capital letters will be used for scalars which are assumed to be real numbers.
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Computing the nearest euclidean distance matrix with low embedding dimensions [PDF]
, 2013 Euclidean distance embedding appears in many high-profile applications including wireless sensor network localization, where not all pairwise distances among sensors are known or accurate.
Qi, Hou-Duo, Yuan, Xiaoming, Qi, Hou Duo
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Visual foundations of Euclidean geometry
Cognitive Psychology, 2021 Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”.
Véronique Izard +2 more
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