Manifold - Charts, Atlases, and Transition Maps

Charts, Atlases, and Transition Maps

Main article: Atlas (topology) See also: Differentiable manifold

The spherical Earth is navigated using flat maps or charts, collected in an atlas. Similarly, a differentiable manifold can be described using mathematical maps, called coordinate charts, collected in a mathematical atlas. It is not generally possible to describe a manifold with just one chart, because the global structure of the manifold is different from the simple structure of the charts. For example, no single flat map can represent the entire Earth without separation of adjacent features across the map's boundaries or duplication of coverage. When a manifold is constructed from multiple overlapping charts, the regions where they overlap carry information essential to understanding the global structure.

Read more about this topic:  Manifold

Famous quotes containing the words transition and/or maps:

    The most remarkable aspect of the transition we are living through is not so much the passage from want to affluence as the passage from labor to leisure.... Leisure contains the future, it is the new horizon.... The prospect then is one of unremitting labor to bequeath to future generations a chance of founding a society of leisure that will overcome the demands and compulsions of productive labor so that time may be devoted to creative activities or simply to pleasure and happiness.
    Henri Lefebvre (b. 1901)

    And now good morrow to our waking souls,
    Which watch not one another out of fear;
    For love all love of other sights controls,
    And makes one little room an everywhere.
    Let sea-discoverers to new worlds have gone,
    Let maps to other, worlds on worlds have shown,
    Let us possess one world; each hath one, and is one.
    John Donne (1572–1631)