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After Gauss, it was still reasonable to think that, although Euclidean geometry was not necessarily true (in the logical sense) it was still empirically true: after all, draw a triangle, cut it up and put the angles together and they will form a straight line.
175, 176): "In his 1926-27 lectures at the University of Warsaw, Alfred Tarski gave an axiomatic development of elementary Euclidean geometry....
For dissimilarities the geometry is contained in the definition, giving the possibility to include physical background knowledge; in contrast to feature-based representations which usually suppose a Euclidean geometry. This paper is devoted to explore dissimilarity representations to classify volcanic-seismic signals.
These map the same reality in different ways, like Euclidean geometry and Riemannian geometry.
These three places are all MADE and do not seek to describe the body but indicate its place, using the Euclidean geometry of architecture in an un-inscribed Arctic environment.
The formula v*w = ||v|| ||w||cos ([theta]) links the algebra of vector coordinates to the Euclidean geometry of lengths and angles, and consequently is a key formula in basic mathematics that enters into numerous mathematical disciplines, both pure and applied.
The view of the covered distance as the area of the figure between the time axis and the velocity curve allows for the use of concepts and propositions of the Euclidean geometry. The use of simple geometric transformations leads to equivalent motion problems of a real context.
Rating films is not akin to Euclidean geometry. The rating board confronts subjectivity--a vapory, inexact witness and, at best, an imprecise measure.
According to Reid, Euclidean geometry is indeed the correct geometry for the objects we touch in the space around us.
Beginning with topological [elastic] geometry and working your way up to Euclidean geometry is a good way to introduce students to the field of geometry.
And his commentary on Plato was contained within his famous thesis that the necessity of Euclidean geometry could find no basis in either hyperouranos or in logic (which Plato himself already knew), but solely within the interior of the subject.