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Concept
Interior Angle
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 angle
s 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
.
Concept
Exterior Angle
An
exterior angle
is formed between one side of a polygon and the extension of an
adjacent side
. The sum of the
exterior angle
s of any polygon is always
360 degrees
, regardless of the
number of sides
.
Concept
Diagonal
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
Vertex
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
.
Concept
Line Segment
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
Polygon
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
Convex Set
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 set
s fundamental in optimization and various
fields of mathematics
, as they exhibit
well-behaved properties
that simplify analysis and computation.
Concept
Concave Set
Concept
Geometric Properties
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.
Concept
Simple Polygon
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 polygon
s are foundational in
computational geometry
, as they are used to model and solve problems related to space and
shape representation
.
Concept
Complex Polygon
Concept
Polygon Triangulation
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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