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Duality. Reality. Shapes/Geometry. Dimensions. Dimensions Videos. Dimensions. A diagram showing the first four spatial dimensions. 1-D: Two points A and B can be connected to a line, giving a new line segment AB. 2-D: Two parallel line segments AB and CD can be connected to become a square, with the corners marked as ABCD. 3-D: Two parallel squares ABCD and EFGH can be connected to become a cube, with the corners marked as ABCDEFGH. 4-D: Two parallel cubes ABCDEFGH and IJKLMNOP can be connected to become a hypercube, with the corners marked as ABCDEFGHIJKLMNOP.
In physical terms, dimension refers to the constituent structure of all space (cf. volume) and its position in time (perceived as a scalar dimension along the t-axis), as well as the spatial constitution of objects within—structures that correlate with both particle and field conceptions, interact according to relative properties of mass—and are fundamentally mathematical in description. The concept of dimension is not restricted to physical objects. A tesseract is an example of a four-dimensional object. Dimension = 1st. One-dimensional geometry[edit] Polytopes[edit] The only regular polytope in one dimension is the line segment, with the Schläfli symbol { }. Hypersphere[edit] where is the radius. Coordinate systems in one-dimensional space[edit] The most popular coordinate systems are the number line and the angle. Length = 2nd Dimension. Bi-dimensional Cartesian coordinate system In physics, our bi-dimensional space is viewed as a planar representation of the space in which we move, described as bi-dimensional space or two-dimensional space.
History of two-dimensional space[edit] Euclid's Elements dealt almost exclusively with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics. The idea of this system was developed in 1637 in writings by Descartes and independently by Pierre de Fermat, although Fermat also worked in three dimensions, and did not publish the discovery.[1] Both authors used a single axis in their treatments and have a variable length measured in reference to this axis.
Two-dimensional geometry[edit] Polytopes[edit] Convex[edit] Degenerate (spherical)[edit] Non-convex[edit] Depth = 3rd Dimension. Three-dimensional Cartesian coordinate system with the x-axis pointing towards the observer(See diagram description for needed correction.) In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. It is commonly represented by the symbol . This space is only one example of a great variety of spaces in three dimensions called 3-manifolds. Details[edit] Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there is an infinite number of possible methods. Another mathematical way of viewing three-dimensional space is found in linear algebra, where the idea of independence is crucial.
Three-dimensional space has a number of properties that distinguish it from spaces of other dimension numbers. With the space , the topologists locally model all other 3-manifolds.
5th Dimensional. 10th Dimension. Dimensional / Sacred Geometry.