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  2. Three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Three-dimensional_space

    A sphere in 3-space (also called a 2-sphere because it is a 2-dimensional object) consists of the set of all points in 3-space at a fixed distance r from a central point P. The solid enclosed by the sphere is called a ball (or, more precisely a 3-ball). The volume of the ball is given by

  3. Holographic principle - Wikipedia

    en.wikipedia.org/wiki/Holographic_principle

    The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region – such as a light-like boundary like a gravitational horizon.

  4. 3-manifold - Wikipedia

    en.wikipedia.org/wiki/3-manifold

    In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer ...

  5. Hyperbolic 3-manifold - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_3-manifold

    Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds).

  6. Lebesgue measure - Wikipedia

    en.wikipedia.org/wiki/Lebesgue_measure

    A subset of R n is a null set if, for every ε > 0, it can be covered with countably many products of n intervals whose total volume is at most ε. All countable sets are null sets. If a subset of R n has Hausdorff dimension less than n then it is a null set with respect to n -dimensional Lebesgue measure.

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  8. Void (astronomy) - Wikipedia

    en.wikipedia.org/wiki/Void_(astronomy)

    A physical significance parameter can be applied in order to reduce the number of trivial voids by including a minimum density to average density ratio of at least 1:5. Subvoids are also identified using this process which raises more philosophical questions on what qualifies as a void. [33] Void finders such as VIDE [34] are based on ZOBOV.

  9. Klein bottle - Wikipedia

    en.wikipedia.org/wiki/Klein_bottle

    A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.