Geometry is a branch of mathematics that is responsible for studying the properties and relationships of geometric figures in space. One of the fundamental concepts in three-dimensional geometry is that of the edge. Edges are key elements that allow us to define and understand the structure of three-dimensional objects.
Definition of edge
In geometry, an edge is a segmented line that forms at the intersection of two surfaces in a three-dimensional object. These surfaces can be flat, curved or any combination of both.
Edges are the visible edges that define the shape of a three-dimensional object and are crucial to understanding its structure. The edges can be straight or curved, and their length can vary from one object to another.
Edge characteristics
1. Length
The length of an edge is the distance between its two ends. This measurement is essential to determine the dimensions of a three-dimensional object and calculate its volume, surface area and other geometric parameters.
2. Direction
Edges have a specific direction in three-dimensional space. This direction is determined by the orientation of the surfaces that intersect to form the edge.
3. Connectivity
Edges connect vertices. A vertex is a point where three or more edges meet. Vertices are critical points in the structure of a three-dimensional object and play an essential role in defining its shape and geometry.
4. Angles
In many cases, the edges form angles to each other. These angles can be right (90 degrees), acute (less than 90 degrees) or obtuse (more than 90 degrees), depending on the arrangement of the surfaces that meet on the edge.
Examples of edges
Flat geometric figures
Below I present some examples of edges in plane geometric figures:
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Triangle: A triangle has three sides. Each of these sides could be considered an "edge" or "side" rather than an edge, since there are no three-dimensional intersections.
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Square: A square has four equal sides. As in the case of a triangle, the sides of the square are considered edges or sides in a plane figure.
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Circle: A circle has no sides or edges in the traditional sense. Instead, it is defined by a continuous curve called a circumference.
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Pentagon: A regular pentagon has five sides. Each of these sides is a line that defines the outline of the pentagon.
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Rectangle: A rectangle has four sides, two of which are equal in length and two of which are equal in length. These sides are considered the edges of the rectangle.
Geometric bodies
examples of edges in some three-dimensional geometric bodies:
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Cube: A cube has 12 edges. Each of these edges is a straight line that connects two vertices of the cube. These edges define the edges of the cube and form the basic structure of the solid.
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Cylinder: A cylinder has two main edges. One is the edge that forms the lateral edge of the cylinder, and the other is the edge that connects the centers of the circular bases. The lateral edge is a curved line, while the edge connecting the centers of the bases is a straight line.
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Pyramid: A pyramid has edges that connect the vertices of its polygonal base with the top vertex. The number of edges in a pyramid depends on the number of sides of the base. For example, a quadrangular pyramid has 8 edges.
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Sphere: Unlike other geometric bodies, a sphere has no edges, since its surface is a continuous curve without edges or vertices. On a sphere, no straight lines can be found connecting different points on its surface.
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Cone: A cone has a lateral edge that is formed at the intersection of its curved lateral surface and its circular base. It also has an edge that connects the vertex of the cone with the center of the base.
Use of edges in geometric calculations
Edges are fundamental elements in geometric calculations. For example, when calculating the volume of a prism, it is necessary to know the length of its edges and how they connect.
Similarly, when calculating the surface area of a three-dimensional object, edges also play a crucial role as they define the boundaries between the faces of the object.