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

... noise ("classic" noise) but with a lower computational overhead, especially in larger

**dimensions**... 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 ...

...

**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 ...

**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" ...

... 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**... 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 ... In three

**dimensions**there are three properties of a bivector that can be interpreted geometrically The arrangement of the plane in space, precisely the attitude of the plane (or alternately ...

... See 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, in which he considered a "point" to be ...

### Famous quotes containing the words dimensions and/or higher:

“It seems to me that we do not know nearly enough about ourselves; that we do not often enough wonder if our lives, or some events and times in our lives, may not be analogues or metaphors or echoes of evolvements and happenings going on in other people?—or animals?—even forests or oceans or rocks?—in this world of ours or, even, in worlds or *dimensions* elsewhere.”

—Doris Lessing (b. 1919)

“The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the *higher* forces.”

—Henry Brooks Adams (1838–1918)