Higher Dimensions

Some articles on higher dimensions, higher, dimensions, dimension:

Link Concordance - Higher Dimensions
... This higher dimensional concordance is a relative form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in N" ...
Eight Queens Puzzle - Related Problems
... Higher dimensions Find the number of non-attacking queens that can be placed in a d-dimensional chess space of size n ... More than n queens can be placed in some higher dimensions (the smallest example is four non-attacking queens in a 3 × 3 × 3 chess space), and it is in fact known that for any k, there are higher ...
Simplex Noise
... computational overhead, especially in larger dimensions ... in 2001 to address the limitations of his classic noise function, especially in higher dimensions ... Simplex noise scales to higher dimensions (4D, 5D) with much less computational cost, the complexity is for dimensions instead of the of classic noise ...
Four-dimensional Space - History
... also n-dimensional space#History The possibility of spaces with dimensions higher than three was first studied by mathematicians in the 19th century ... In 1827 Möbius realized that a fourth dimension would allow a three-dimensional form to be rotated onto its mirror-image, and by 1853 Ludwig Schläfli had discovered many polytopes in higher dimensions ... Higher dimensions were soon put on firm footing by Bernhard Riemann's 1854 Habilitationsschrift, Über die Hypothesen welche der Geometrie zu Grunde liegen ...
Bivector - Three Dimensions - Geometric Interpretation
... This can be described in any dimension but is best done in three where parallels can be drawn with more familiar objects, before being applied to higher dimensions ... In two dimensions the geometric interpretation is trivial, as the space is two dimensional so has only one plane, and all bivectors are associated with it differing only by a ... In three dimensions there are three properties of a bivector that can be interpreted geometrically The arrangement of the plane in space, precisely ...

Famous quotes containing the words dimensions and/or higher:

    The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.
    Thomas Jefferson (1743–1826)

    What is termed Sin is an essential element of progress. Without it the world would stagnate, or grow old, or become colourless. By its curiosity Sin increases the experience of the race. Through its intensified assertion of individualism it saves us from monotony of type. In its rejection of the current notions about morality, it is one with the higher ethics.
    Oscar Wilde (1854–1900)