Eight-dimensional Euclidean space is eight-dimensional space equipped with a Euclidean metric, which is defined by the dot product.
More generally the term may refer to an eight-dimensional vector space over any field, such as an eight-dimensional complex vector space, which has 16 real dimensions.
It may also refer to an eight-dimensional manifold such as an 8-sphere, or a variety of other geometric constructions.
Mathematically they can be specified by 8-tuplets of real numbers, so form an 8-dimensional vector space over the reals, with addition of vectors being the addition in the algebra.
A normed algebra is one with a product that satisfies for all x and y in the algebra.
A normed division algebra additionally must be finite-dimensional, and have the property that every non-zero vector has a unique multiplicative inverse.
In spite of the frequently stated phrases that "all radiation is harmful" and that "there is no safe dose of radiation", we humans contain, survive, and thrive with rather remarkable quantities of radioactive materials in our bodies.
In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space.
When n = 8, the set of all such locations is called 8-dimensional space.
Often such spaces are studied as vector spaces, without any notion of distance.
The most studied are the regular polytopes, of which there are only three in eight dimensions: the 8-simplex, 8-cube, and 8-orthoplex.
A broader family are the uniform 8-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group.