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Personal autonomy refers to an individual's capacity to make informed, uncoerced decisions about their own life, reflecting their values and beliefs. It is a fundamental aspect of human dignity and is essential for the exercise of personal freedom and responsibility.
An interior angle is the angle formed between two sides of a polygon that share a common vertex, lying inside the shape. The sum of the interior angles of a polygon depends on the number of sides and can be calculated using the formula (n-2) × 180°, where n is the number of sides.
An exterior angle is formed between one side of a polygon and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.
Concept
A diagonal is a straight line connecting non-adjacent vertices in a polygon or a polyhedron, effectively bridging corners that are not directly next to each other. This concept is pivotal in geometry for calculating distances, understanding shapes, and solving problems related to angles and symmetry.
Concept
A vertex is a fundamental element in geometry and graph theory, representing a corner or intersection point where two or more lines, edges, or curves meet. In the context of graphs, a vertex is a node that may connect to other vertices via edges, playing a crucial role in the structure of networks and geometric shapes.
A line segment is a part of a line bounded by two distinct endpoints, and it contains every point on the line between its endpoints. It is the simplest form of a geometric shape and serves as a fundamental building block in geometry, connecting points and forming the sides of polygons.
Concept
A polygon is a two-dimensional geometric figure with a finite number of straight sides that are fully closed to form a shape. Polygons are categorized by the number of sides they have, such as triangles, quadrilaterals, and pentagons, and play a fundamental role in geometry and computer graphics.
Concept
A convex set is a subset of a vector space where, for any two points within the set, the line segment connecting them is entirely contained within the set. This property makes convex sets fundamental in optimization and various fields of mathematics, as they exhibit well-behaved properties that simplify analysis and computation.
Geometric properties are characteristics that define the shape, size, and relative position of figures in space, often used to determine congruence, similarity, and symmetry. These properties play a crucial role in various fields such as mathematics, physics, engineering, and computer graphics, where they help in modeling and analyzing physical structures and phenomena.
A simple polygon is a flat shape consisting of straight, non-intersecting line segments or 'sides' that are connected to form a closed path. simple polygons are foundational in computational geometry, as they are used to model and solve problems related to space and shape representation.
Polygon triangulation is the process of dividing a polygon into a set of triangles, which is a fundamental operation in computational geometry that aids in simplifying complex polygonal shapes for easier processing and analysis. This technique is crucial for applications in computer graphics, finite element analysis, and geographical information systems, where efficient rendering and data representation are necessary.
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