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These grid squares cut the given polygon into pieces, which can be rearranged (by matching up pairs of squares along each edge of the polygon) into a polyomino with the same area. [ 14 ] Pick's theorem may also be proved based on complex integration of a doubly periodic function related to Weierstrass elliptic functions .
The dot planimeter is physical device for estimating the area of shapes based on the same principle. It consists of a square grid of dots, printed on a transparent sheet; the area of a shape can be estimated as the product of the number of dots in the shape with the area of a grid square. [8]
Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.
When counting dots near the boundary of the shape as 1/2, there are 69 interior dots and 20 boundary dots for an estimated area of 79, close to the actual area of 25 π ≈ 78.54. A dot planimeter is a device used in planimetrics for estimating the area of a shape , consisting of a transparent sheet containing a square grid of dots.
The fact that the no-three-in-line problem has a solution with linearly many points can be translated into graph drawing terms as meaning that every graph, even a complete graph, can be drawn without unwanted vertex-edge incidences using a grid whose area is quadratic in the number of vertices, and that for complete graphs no such drawing with ...
A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. [1] [2] [3] Spreadsheets were developed as computerized analogs of paper accounting worksheets. [4] The program operates on data entered in cells of a table.
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]
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