Sentence examples for relation of geometry from inspiring English sources

The pre-Socratics thus revealed difficulties in specific assumptions about the infinitely many and the infinitely small and about the relation of geometry to physical reality, as well as in more general conceptions like "existence" and "proof".

The classical theory of physical geometry, developed by Helmholtz, Poincaré and Hilbert, regarded the concept of "metric congruence" as the only basic relation of geometry, and constructed physical geometry from this one notion alone in terms of the relative positions and displacements of physical congruence standards.

By using the projection relation of differential geometry, the optimal path generation algorithm of the Bézier surface based on Hilbert fractal polishing path is established.

Besides being translated, a co-ordinate system may also be rotated.2 This signifies analytically: the relations of Euclidean geometry are covariant with respect to linear orthogonal transformations of the co-ordinates.

Movements are designed to either be task-relevant, capturing some key relation of the subsequent geometry conjecture (Table 1), or task-irrelevant.

One example of this subordination is found in the relation between the science of geometry and its subordinate sciences.

With respect to the relation of postulates to theorems, geometry is thus analytic, like any other rigorously deductive discipline.

Recall our explanation of the relation between geometry and topology at the very beginning of this rebuttal: topology can be inferred from geometry, but geometry cannot be inferred from topology.

Geometric dilution of precision (GDOP), a relatively convenient indicator calculated on the basis of Cramer-Rao bound (CRB), is commonly used to describe the influence of geometry on the relation between the position determination error and the measurement error [26 31].

The principles of geometry thus express relations among basic geometric concepts inasmuch as these can be "exhibited in intuition" (Shabel 2003, Sutherland 2005a).

The results suggest that learning the position of a goal in relation to the geometry of the environment can be blocked but only by an alternative geometric cue.