This term is used in geography to designate the extension or area of a territory, while in mathematics it defines that which only has length and width. For mathematics, a surface is a set of points in a Euclidean space that form a two-dimensional space.
It is a metric concept that assigns a measure to the extension of a surface. It is expressed in mathematics as units of area. It is a metric concept that requires the specification of a measure of length. The area of curved surfaces can be calculated with differential geometry methods. The area is the measure that gives the size of a region enclosed by a geometric figure.
The area is an ancient concept that was born with the Egyptians, who had to calculate the area of their agricultural plots to restore their limits after the floods of the Nile. To calculate the area of a polygon, add the area of all the triangles that make it up , this method was proposed by the Greek sage Antiphon around the year 430 BC. C. From this method it derives that any flat surface with straight sides or polygon can be triangulated allowing its area to be calculated.
Differences between surface and area
- Surfaces are a geometric concept that defines a set of points tangent to each other that occupy a two-dimensional space.
- The area is the metric magnitude associated with the geometric concept.