On Angular Measures in Axiomatic Euclidean Planar Geometry
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of measuring a plane ...
Grötschel Martin+3 more
doaj +1 more source
Pseudo-Riemannian geodesics and billiards [PDF]
Many classical facts in Riemannian geometry have their pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while ...
Khesin, B., Tabachnikov, S.
core +2 more sources
The paper discusses the role of scale anomaly in generating edge electric currents via the scale magnetic effect in scalar electrodynamics. Although the boundary electric current is much weaker than the Meissner current induced in superconducting materials, the scale anomaly can enhance conductivity near the boundary of the material.
Maxim Chernodub+2 more
wiley +1 more source
An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape [PDF]
A major concern in South Africa is the poor performance of learners in mathematics, particularly in geometry. This paper therefore sought to explore the learners’ understanding of Euclidean geometric concepts.
Thabisa Maqoqa
doaj +1 more source
The use of semiotic representations in reasoning about similar triangles in Euclidean geometry
Mathematics outcomes in South Africa are very low and many researchers and stakeholders have expressed concerns about the poor performance in mathematics at school level, especially in geometry (Luneta, 2015; Mthembu, 2007; Singh, 2006; Van Putten, Stols
I. Ubah, S. Bansilal
semanticscholar +1 more source
Do mito da Geometria Euclidiana ao ensino das Geometrias Não Euclidianas
Das tentativas frustradas de provar que o quinto postulado de Euclides era um teorema, surgiram as Geometrias Não Euclidianas. Com os quatro primeiros postulados de Euclides e a negação do quinto, surgiram outras Geometrias cujos postulados são possíveis
Mylane dos Santos Barreto+1 more
doaj +1 more source
Impacts of implementing geogebra on eleventh grade student’s learning of Euclidean Geometry
The aim of the study was to evaluate the efficiency of applying GeoGebra software as a teaching tool to enhance high poverty, rural grade 11 students’ understanding of Euclidean geometry circle theorems. The experimental group received instruction on how
A. Bayaga+3 more
semanticscholar +1 more source
Object tracking via non-Euclidean geometry: A Grassmann approach [PDF]
A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image.
S. Shirazi+3 more
semanticscholar +1 more source
Embryonic cranial cartilage defects in the Fgfr3Y367C/+ mouse model of achondroplasia
Abstract Achondroplasia, the most common chondrodysplasia in humans, is caused by one of two gain of function mutations localized in the transmembrane domain of fibroblast growth factor receptor 3 (FGFR3) leading to constitutive activation of FGFR3 and subsequent growth plate cartilage and bone defects.
Susan M. Motch Perrine+9 more
wiley +1 more source
Distances between fixed-point sets in 2-dimensional Euclidean buildings are realised [PDF]
We prove that if two finitely generated groups act on a metrically complete 2-dimensional Euclidean building, then the distance between their fixed-point sets is realised. Our proof uses the geometry of Euclidean buildings, which we view as CAT(0) spaces, and properties of ultrapowers of Euclidean buildings.
arxiv