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  4. Dashura Reply
    Integral Calculus, The Volume of the Hypersphere The Volume of the Hypersphere The sphere in n dimensions is the set of points that are 1 unit away from the origin. In 3 space the sphere has the equation x 2 +y 2 +z 2 = 1. In the previous section we calculated the volume of this sphere. Is there a formula for the volume of the unit sphere in n.
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    A study of the 4-dimensional object known as the hypersphere (a 4-dimensional sphere). Included is a detailed description of how the surface of a hypersphere lies at a right angle to our dimension, and an explanation of how a hypersphere curves into the fourth dimension.
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  9. JoJokinos Reply
    Jan 10,  · There are several books and other references that can help you visualize the fourth spatial dimension, but it's extremely difficult. There was a guy from late 19th or early 20th century, I believe, who had worked out a system involving a set of blocks with colors on the different faces, along with edge and vertex labels that allowed him to visualize in 4 dimensions.
  10. Nejinn Reply
    The term hypersphere was introduced by Duncan Sommerville in his discussion of models for non-Euclidean geometry. The first one mentioned is a 3-sphere in four dimensions. Some spheres are not hyperspheres: If S is a sphere in E m where m hypersphere.

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