3 Conversion of light travel distances to

Euclidean distances

1 for the Poincare plane) show that there exist self-concordant functions on Riemannian manifolds which cannot be represented as self-concordant functions in

Euclidean spaces.

A

Euclidean measurement by definition will always be equal to or lesser than a DriveDistance measurement to and from the same locations; however, the magnitude of this difference is unknown.

Thus for the

Euclidean weight, there may be one or two entries from [Z.

As suggested above, if all lines are guaranteed to meet at one point, the study of intersections does not have to make any exceptions (a flaw of

Euclidean Geometry).

Terras, Finite analogues of

Euclidean space, Journal of Computational and Applied Mathematics, 68 (1996), 221-238.

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.

In this world of the word there can be no question of the

Euclidean law filling every corner of the verbal space.

A typical vector buffer function in GIS is based on 2D

Euclidean distance instead of surface (or slope) distance, resulting in an inaccurate representation of buffers when they are verified in the field.

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.

Odio frees her characters, allowing them to leave

Euclidean space and enter instead into a new and unknown cosmic conscience.

As McClintock, paraphrasing Lincoln, remarked, ``You cannot disprove

Euclidean geometry by calling Euclid a liar.