Many of the theorems of

Euclidean geometry are relatively similar form in the Einstein relativistic velocity model, Aubel's theorem for gyrotriangle is an example in this respect.

or structures included in other structures, geometric multispaces (combinations of

Euclidean and Non-

Euclidean geometries into one space as in S-geometries), theoretical physics, including the Relativity Theory [4], the M-theory and the cosmology, then multi-space models for p-branes and cosmology, etc.

For the scenario with a model of the motion of the photon in an expanding space, the

Euclidean distances were fed into the sampling volume formula.

An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in

Euclidean space.

Humans made a mark without destroying nature, enhancing it by making a

Euclidean statement on the raw wilderness, which made its mysteries more awesome and gave it dimension, direction, making it comprehensible.

In fact, if one recognizes Lobatschewsky's and Riemann's systems as descriptions of physical space that are closer to the truth than Euclid's--something that Einstein's relativity seems to suggest--then one cannot attribute to the

Euclidean system universal and necessary validity.

If we consider on M = (0, [infinity]) the

Euclidean metric g(x) = 1, then the self-concordance condition for the same function f leads to k [greater than or equal to] 1.

Projects ranging from

Euclidean mathematics to the Chinese economy have been submitted by the AQA examinations board.

These distances can be estimated using either

Euclidean (i.

In Section 2 of this paper we obtain Plotkin's bound for linear codes equipped with the

Euclidean weight function.

The second chapter discusses the failures of traditional

Euclidean zoning, including unnecessary complexity, a moiety of false assumptions, and lock of flexibility in implementation.

Before hyperbolic geometry was discovered, it was thought to be completely obvious that

Euclidean geometry correctly described physical space, and attempts were even made, by Kant and others, to show that this was necessarily true.

Manhattan metric, also known as the 12 norm, measures distance similar to the Manhattan district of New York- where as typically in

Euclidean metric, one can move in any direction a set distance from center in a circle, in Manhattan metric one can only move one unit north or south, east or west, resulting in a diamond shape.

In Section 3, we construct our main tools to study simplexes in vector spaces over finite fields, the finite

Euclidean and non-

Euclidean graphs.

The most well-known are the Rectangular Distance Metric (a = 1) and the

Euclidean Distance Metric (a = 2).