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In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles .
Gran Atlas Aguilar (Spain, 1969/1970) Historical Atlas of China (Taiwan, 1980) The Historical Atlas of China (China, 1982) National Geographic Atlas of the World (United States, 1963–present) Pergamon World Atlas (1962/1968) Times Atlas of the World (United Kingdom, 1895–present) Dorling Kindersley Atlas of the World 1994–present
The ratio of the measured lines then gives the component value as a fraction of 100%. A displacement along a parallel line (grid line) preserves the sum of two values, while motion along a perpendicular line increases (or decreases) the two values an equal amount, each half of the decrease (increase) of the third value.
Theatrum Orbis Terrarum (Latin: [tʰɛˈaːtrũː ˈɔrbɪs tɛˈrːaːrũː], "Theatre of the Lands of the World") is considered to be the first true modern atlas.Written by Abraham Ortelius, strongly encouraged by Gillis Hooftman [2] and originally printed on 20 May 1570 in Antwerp, [3] it consisted of a collection of uniform map sheets and supporting text bound to form a book for which ...
The multiplication of two complex numbers can be expressed most easily in polar coordinates — the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as ...
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced it in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] (aka.
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
The remaining two half-lines in the two X s can be linked to each other in two ways, so that the total number of ways to form the diagram is 4 × 3 × 4 × 3 × 2 × 2, while the denominator is 4! × 4! × 2!. The total symmetry factor is 2, and the contribution of this diagram is divided by 2.