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Although map making and use of the grid existed in China before him, [43]: 106–107 he was the first to mention a plotted geometrical grid and graduated scale displayed on the surface of maps to gain greater accuracy in the estimated distance between different locations.
A 3-map graph is a planar graph, and every planar graph can be represented as a 3-map graph. Every 4-map graph is a 1-planar graph, a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map ...
Mairie de Loevenich (), from the Topographic Survey of the Rhineland by Tranchot/Müffling, sheet 57 (published 1806/07).. A map series is a group of topographic or thematic charts or maps usually having the same scale and cartographic specifications, and with each sheet appropriately identified by its publisher as belonging to the same series.
The multiplication sign (×), also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product. [ 1 ] The symbol is also used in botany , in botanical hybrid names .
In graph-theoretic terms, the theorem states that for a loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
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