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Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are called 3-manifolds. The term may also refer colloquially to a subset of space, a three-dimensional region (or 3D domain), [1] a solid figure.
Geodesy or geodetics [1] is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D.It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. [2]
Topography is a field of geoscience and planetary science and is concerned with local detail in general, including not only relief, but also natural, artificial, and cultural features such as roads, land boundaries, and buildings. [1]
More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not self-crossing curves such as a figure 8.
Also amphidrome and tidal node. A geographical location where there is little or no tide, i.e. where the tidal amplitude is zero or nearly zero because the height of sea level does not change appreciably over time (meaning there is no high tide or low tide), and around which a tidal crest circulates once per tidal period (approximately every 12 hours). Tidal amplitude increases, though not ...
The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space ...
In all dimensions, the fundamental group of a manifold is a very important invariant, and determines much of the structure; in dimensions 1, 2 and 3, the possible fundamental groups are restricted, while in dimension 4 and above every finitely presented group is the fundamental group of a manifold (note that it is sufficient to show this for 4- and 5-dimensional manifolds, and then to take ...
Three commonly used (but different) center points are: the mean center, also known as the centroid or center of gravity; the median center, which is the intersection of the median longitude and median latitude; the geometric median, also known as Weber point, Fermat–Weber point, or point of minimum aggregate travel.