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    Four-dimensional space - Wikipedia

    Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, … 展开

    Lagrange wrote in his Mécanique analytique (published 1788, based on work done around 1755) that mechanics can be viewed as operating in a four-dimensional space— three … 展开

    In the familiar three-dimensional space of daily life, there are three coordinate axes—usually labeled x, y, and z—with each axis orthogonal (i.e. perpendicular) to the other two. The six cardinal … 展开

    Research using virtual reality finds that humans, despite living in a three-dimensional world, can, without special practice, make spatial judgments about line segments embedded … 展开

    In art
    In literature
    Science fiction texts often mention the concept of "dimension" when referring to parallel or alternate universes 展开

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    Dimensional analogy 图像

    Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to 展开

    The geometry of four-dimensional space is much more complex than that of three-dimensional space, due to the extra degree of freedom.
    Just as in three dimensions there are polyhedra made of two dimensional polygons, … 展开

    To understand the nature of four-dimensional space, a device called dimensional analogy is commonly employed. Dimensional analogy is the study of how (n − 1) … 展开

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  4. The HyperSphere - Massachusetts Institute of …

    Learn about the hypersphere, a four dimensional object that has properties both similar to and different from the ordinary sphere. See how to project and visualize shapes on the hypersphere, such as the dodecahedron, using stereographic …

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