Tool to apply and calculate a surface using the Pick's Theorem that allows the calculation of the area of a polygon positioned on a lattice (normalized orthogonal grid) and whose vertices are points of the grid.

Pick's Theorem - dCode

Tag(s) : Geometry

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Pick's Theorem is a mathematical formula that allows you to calculate the area of a polygon whose vertices have integer coordinates in a Cartesian plane (a 2D grid/grid).

For a polygon with $ b $ vertices constructed on a grid (the vertices are grid points) having $ i $ points inside it, Pick's formula indicates that the area $ A $ of the polygon is $$ A = i + \frac{b}{2} - 1 $$

All points present on the contour are considered vertices (vertex angles are flat in this case).

Pick's formula requires two parameters: the number $ i $ of interior points of the polygon and the number $ b $ of points on the contour/perimeter of the polygon. The area $ A $ of the polygon is $ A = i + \frac{b}{2} - 1 $

Yes, Pick's Theorem can be applied to concave polygons as long as the vertices have integer coordinates.

Pick's Theorem only applies to simple polygons with no holes inside. However, if the hole(s) form a polygon eligible for Pick's Theorem, then it is possible to calculate the area of the hole polygon (ignoring the holes) and subtract the areas of the holes to obtain the area of the hole. polygon with holes.

The formula owes its name to Georg Alexander Pick who described it in 1899.

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Cite as source (bibliography):

*Pick's Theorem* on dCode.fr [online website], retrieved on 2024-06-15,

pick,theorem,polygon,area,surface,grid,vertex,vertice,point

https://www.dcode.fr/pick-theorem

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