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The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [1]
The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10] Of all n-gons with given side lengths, the one with the largest area is cyclic. Of all n-gons with a given perimeter, the one with the largest area is regular (and therefore ...
A net of a regular dodecahedron The eleven nets of a cube. In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.
A definite integral of a function can be represented as the signed area of the region bounded by its graph and the horizontal axis; in the above graph as an example, the integral of () is the yellow (−) area subtracted from the blue (+) area
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Such an area is called the signed area of the parallelogram: the absolute value of the signed area is the ordinary area, and the sign determines its orientation. The fact that this coefficient is the signed area is not an accident.