Planar
In mathematics, the term “planar” refers to objects or shapes that lie in a single flat plane
In mathematics, the term “planar” refers to objects or shapes that lie in a single flat plane. This means that all points, lines, and figures in a planar geometry can be contained within a single two-dimensional surface, without any intersecting or overlapping.
In a planar graph, the nodes or vertices and the edges are all situated in a single plane. This type of graph is commonly used to represent and study various networks, such as social networks or transportation systems, where the connections between different entities can be represented by edges.
In geometry, a planar figure is a shape that can be formed on a single plane. Examples of planar figures include triangles, rectangles, circles, and polygons. These figures have well-defined dimensions, such as length, width, and area, and they can be easily visualized on a flat surface.
Planar graphs and planar figures have several important properties and characteristics. For instance, a planar graph can be drawn without any crossing edges, whereas a non-planar graph cannot be drawn in such a way. Similarly, planar figures have well-defined areas and perimeters, and they can be easily manipulated and analyzed using various geometric formulas and theorems.
The study of planar geometry, including planar graphs and planar figures, plays a significant role in many branches of mathematics, such as graph theory, topology, and geometry. It provides a foundation for understanding and analyzing a wide range of mathematical concepts and applications.
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