atlas
American Heritage Dictionary:
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at·las1
(ăt'ləs) 
n., pl., -las·es.
at·las2 (ăt'ləs)
n., pl., -es.
n., pl., -las·es.
- A book or bound collection of maps, sometimes with supplementary illustrations and graphic analyses.
- A volume of tables, charts, or plates that systematically illustrates a particular subject: an anatomical atlas.
- A large size of drawing paper, measuring 26 × 33 or 26 × 34 inches.
[After Atlas, probably from depictions of him holding the world on his shoulders that appeared on the frontispieces of early works of this kind.]
at·las2 (ăt'ləs)
n., pl., -es.
- pl., at·lan·tes (ăt-lăn'tēz). Architecture. A standing or kneeling figure of a man used as a supporting column, as for an entablature or balcony.
- Anatomy. The top or first cervical vertebra of the neck, which supports the skull.
[From ATLAS.]
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The first intercontinental ballistic missile built by the United States, tested in 1958 and deployed in 1959. See also Minuteman.
See the Introduction, Abbreviations and Pronunciation for further details.
Columbia Encyclopedia:
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Atlas
atlas, in geography, collection of maps or charts. It usually includes data on various features of a country, e.g., its topography, natural resources, climate, and population, as well as its agriculture and main industries. In astronomy, a star atlas is a collection of maps or photographs covering much or all of the celestial sphere and showing the locations of stars and other objects. Although the first known atlas was compiled by the Greek geographer Ptolemy in the 2d cent. A.D., its modern form was introduced in 1570 with the publication of Theatrum orbis terrarum by the Flemish geographer Abraham Ortelius. In 1595 his close friend Gerardus Mercator published Atlas sive cosmographicae. Its frontispiece was a figure of the titan Atlas holding a globe on his shoulders. The name Atlas subsequently came to be applied to volumes of maps and information in this format.
A bound collection of maps. Atlases are named after the Greek god Atlas.
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The first cervical vertebra, the uppermost segment of the backbone which supports the skull, characterized by the absence of a body and a wide vertebral canal.
Random House Word Menu:
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categories related to 'atlas'
- Maps and Cartography - atlas: bound maps showing different parts of world
- Publications - atlas: book of maps and charts
- Books and Pages - atlas: book of maps and geographical charts
Wikipedia on Answers.com:
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Atlas (topology)
- For other uses of "atlas", see Atlas (disambiguation).
In mathematics, particularly topology, one describes a manifold using an atlas. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. If the manifold is the surface of the Earth, then an atlas has its more common meaning. In general, the notion of atlas underlies the formal definition of a manifold.
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Contents
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Charts
The definition of an atlas depends on the notion of a chart. A chart for a topological space M is a homeomorphism 
from an open subset U of M to an open subset of Euclidean space. The chart is traditionally recorded as the ordered pair 
.
Formal definition of atlas
An atlas for a topological space M is a collection 
of charts on M such that 
. If the range of each chart is the n-dimensional Euclidean space, then M is said to be an n-dimensional manifold.
Transition maps
A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other. This composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. (For example, if we have a chart of Europe and a chart of Russia, then we can compare these two charts on their overlap, namely the European part of Russia.)
To be more precise, suppose that 
and 
are two charts for a manifold M such that 
is non-empty. The transition map 
is the map defined on the intersection by
Note that since 
and 
are both homeomorphisms, the transition map is also a homeomorphism.
More structure
One often desires more structure on a manifold than simply the topological structure. For example, if one would like an unambiguous notion of differentiation of functions on a manifold, then it is necessary to construct an atlas whose transition functions are differentiable. Then one can unambiguously define the notion of tangent vectors and then directional derivatives.
If each transition function is a smooth map, then the atlas is called a smooth atlas. Alternatively, one could require that the transition maps have only k continuous derivatives in which case the atlas is said to be 
.
Very generally, if each transition function belongs to a pseudo-group 
of homeomorphisms of Euclidean space, then the atlas is called a -atlas.
References
- Lee, John M. (2006). Introduction to Smooth Manifolds. Springer-Verlag. ISBN 978-0-387-95448-6.
- Sepanski, Mark R. (2007). Compact Lie Groups. Springer-Verlag. ISBN 978-0-387-30263-8.
External links
- Atlas by Rowland, Todd
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
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Atlas
Dansk (Danish)
1.
n. - atlas, kortbog
2.
n. - atlashvirvel, øverste halshvirvel
n. - Atlas
Nederlands (Dutch)
atlas, bovenste halswervel, steunpilaar
Français (French)
1.
n. - (Géog) atlas, (Anat) atlas, atlas (un format), (Archit) atlante, télamon
2.
n. - (Mythol) Atlas, (Monts) de l'Atlas
Deutsch (German)
1.
n. - Atlas
2.
n. - Atlasseide
n. - Atlas
Ελληνική (Greek)
n. - 'Ατλας, (γεωγραφικός) άτλαντας, άτλας, (ανατ.) άτλας, επιστροφέας
Português (Portuguese)
n. - atlas (m)
Русский (Russian)
атлас, титан, могучая опора, карта
Español (Spanish)
1.
n. - atlas
2.
n. - atlante
Svenska (Swedish)
n. - atlas, kartbok, atlas (med.)
中文（简体）(Chinese (Simplified))
1. 地图集, 图解集
2. 巨神阿特拉斯, 身负重担的人
中文（繁體）(Chinese (Traditional))
1.
n. - 地圖集, 圖解集
2.
n. - 巨神阿特拉斯, 身負重擔的人
한국어 (Korean)
1.
n. - 지도책, 대역, 미국의 우주 개발용 로켓
2.
n. - 아틀라스(신들을 배반한 죄로 하늘을 짊어지게 된 신)
日本語 (Japanese)
n. - 地図帳, 図解, アトラス, 図表集, アトラス判
العربيه (Arabic)
(الاسم) أطلس, مصور جغرافي , مجموعه خرائط جغرافيه مجلده, الفهقه : فقهرة العنق الأولى
עברית (Hebrew)
n. - אטלס, מפון
n. - חוליית הצוואר
n. - אטלס
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American Heritage Dictionary
The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.
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The Columbia Electronic Encyclopedia, Sixth Edition Copyright © 2012, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/.
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The New Dictionary of Cultural Literacy, Third Edition Edited by E.D. Hirsch, Jr., Joseph F. Kett, and
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This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article Atlas (topology).
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