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The area of a polygon is the measurement of the 2-dimensional region enclosed by the polygon.
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area and polygon
Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.
Territorial sea: irregular polygon extending up to 100 nautical miles ( 185 km ) from coastline as defined by 1898 treaty ; since late 1970s has also claimed polygonal-shaped area in South China Sea up to 285 nautical miles ( 528 km ) in breadth.
For a non-self-intersecting ( simple ) polygon with n vertices, the area and centroid are given by:
As one wraps around the polygon, these triangles with positive and negative area will overlap, and the areas between the origin and the polygon will be cancelled out and sum to 0, while only the area inside the reference triangle remains.
The area A of a simple polygon can also be computed if the lengths of the sides, a < sub > 1 </ sub >, a < sub > 2 </ sub >, ..., a < sub > n </ sub > and the exterior angles, θ < sub > 1 </ sub >, θ < sub > 2 </ sub >, ..., θ < sub > n </ sub > are known.
If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
In every polygon with perimeter p and area A, the isoperimetric inequality holds.
If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon.
The area of a regular polygon is also given in terms of the radius r of its inscribed circle and its perimeter p by
The sides of a polygon do not in general determine the area.
However, if the polygon is cyclic the sides do determine the area.
The area of a self-intersecting polygon can be defined in two different ways, each of which gives a different answer:
* Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region.
This corresponds to the area of the plane covered by the polygon, or to the area of a simple polygon having the same outline as the self-intersecting one ( or, in the case of the cross-quadrilateral, the two simple triangles ).
Such a polygon does not have to lie in a plane, or have straight sides, or enclose an area, and individual elements can overlap or even coincide.
The area of any polygon on a sphere is proportional to the polygon's angle excess, with the proportionality constant being the square of the sphere's radius when the angle excess is given in radians.
area and is
Sensibility is a vague word, covering an area of meaning rather than any precise talent, quality, or skill.
I suppose the day will inevitably come when the area will be encrusted with developments, but at present it is deserted and seductive.
Diplomatic is another area for which the dawn of the twentieth century marks the beginning of modern standards of scholarship.
Therefore, what we must prove or disprove is that there were Saxons, in the broad sense in which we must construe the word, in the area of the Saxon Shore at the time it was called the Saxon Shore.
Easily the best known of these three novels is The Space Merchants, a good example of a science-fiction dystopia which extrapolates much more than the impact of science on human life, though its most important warning is in this area, namely as to the use to which discoveries in the behavioral sciences may be put.
Underlying these hopes and prescriptions is a conviction that the nations of the North Atlantic area do indeed form a community, at least a potential community.
Now the park is filled with marble busts and all the streets in the immediate area have the full and proper names of the men who fell.
The move for establishment of a national seashore park on 30,000 acres of Cape Cod, from Provincetown to Chatham, is strengthened by President Kennedy's interest in that area.
First of all there is ample area in East Greenwich already zoned in the classification similar to that which petitioner requested.
I believe it is an area in which professional planners have failed to set adequate guide posts ; ;
But this we know: Here is a great life that in every area of American politics gives the American people occasion for pride and that has invested the democratic process with the most decent qualities of honor, decency, and self-respect.
Not only is this kind of duplication wasteful, but it gives the combined system the ability to take freight traffic away from the New York Central and other railroads serving the area.
The shelter illustrated in figure 12 is based on such a room built in a new home in the Washington, D.C. area in the Spring of 1959.
The objective is to achieve sufficient effectiveness of control on all of the area now under treatment plus the additional acres so that after the initial period only maintenance control will be needed.
By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.
During nighttime hours, because of the intense skywave propagation then prevailing, no large number of stations can be permitted to operate on one of these channels, if the wide area service for which these frequencies are assigned is to be rendered satisfactorily by the dominant stations which must be relied upon to render it.
The area available at Heywood is approximately three times the size of the former Rochdale and Manchester locations.
As you can see, in this Push-Pull Super Set the entire chest-back-shoulder area is vigorously exercised in alternate sectors by alternate exercises so the complete torso remains pumped-up all the time!!
By this time Henri's entire chest-back-lat-shoulder area is pumped-up to almost bursting point, and Claude takes time to do a bit more pectoral-front deltoid shaping work.
The cross-sectional area of the cylinders is determined and then the volume of the individual cylinders is computed by multiplying the area by the stroke length, which is the equivalent of the length of the cylinders.
area and measurement
Therefore, the on-the-scene commander must have detailed operating instructions based on measurement of conditions, in the area, at the time of encounter.
All of these techniques are extremely noise-prone and / or subject to bias in the biological measurement, and a major research area in computational biology involves developing statistical tools to separate signal from noise in high-throughput gene expression studies.
Within each of these maturity levels are Key Process Areas which characterise that level, and for each such area there are five factors: goals, commitment, ability, measurement, and verification.
The term " Geiger counter " is commonly used to mean a hand-held survey type meter, however the Geiger principle is in wide use in installed " area gamma " alarms for personnel protection, and in process measurement and interlock applications.
Over the intervening 70 years, the problem of measurement became an active research area and itself spawned some new formulations of quantum mechanics.
Many areas of study are still in development, specifically in the area of performance measurement.
Instrumentation is defined as the art and science of measurement and control of process variables within a production or manufacturing area.
Choosing a unit of measurement so that the seven pieces can be assembled to form a square of side one unit and having area one square unit, the seven pieces are:
This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who attempted to reconcile some of the apparent inconsistencies of classical boolean logic with the facts related to measurement and observation in quantum mechanics.
The other state tax credit programs are smaller in dollar measurement, but are very significant in the area and the conservation values that they cause to be protected.
The caesium magnetometer's faster measurement rate allows the sensor to be moved through the area more quickly for a given number of data points.
: b A virgate was a unit of land area measurement used in medieval England, and was held to be the amount of land that a team of two oxen could plough in a single annual season.
Radio stations Monterey-Salinas-Santa Cruz area of dominant influence ( ADI ) or continuous measurement market ( CMM ).
According to the United States Census Bureau, the CDP has a total area of, all of it land ( this measurement seems to exclude Astor's network of canals, which extends over in length, providing river access for many of its residents.
The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.
The physics term " barn ", which is a subatomic unit of area, 10 < sup >− 28 </ sup > m < sup > 2 </ sup >, came from experiments with uranium nuclei during World War II, wherein they were described colloquially as " big as a barn ", with the measurement officially adopted to maintain security around nuclear weapons research.
Population density ( in agriculture standing stock and standing crop ) is a measurement of population per unit area or unit volume.
The Scoliosis Research Society's recommendations for bracing include curves progressing to larger than 25 °, curves presenting between 30 and 45 °, Risser sign 0, 1, or 2 ( an X-ray measurement of a pelvic growth area ), and less than six months from the onset of menses in girls.
Many theories have been proposed since the beginning of quantum mechanics and quantum measurement continues to be an active research area in both theoretical and experimental physics.
In terrestrial ecosystems, mass of carbon per unit area per year ( g C / m < sup > 2 </ sup >/ yr ) is most often used as the unit of measurement.
The cross-sectional area of the flow is calculated from a depth measurement and the average velocity of the flow is measured directly ( Doppler and propeller methods are common ).
This measurement includes a training area of unspecified size.
2D measurement of the diameter ( d ) of the aortic annulus allows calculation of the flow CSA ( cross-sectional area ) which is then multiplied by the vti of the Doppler flow profile across the aortic valve to determine the flow volume or SV.
* Wire gauge, a measurement of the cross-sectional area of a wire
0.174 seconds.