# area

(redirected from AUC)
Also found in: Dictionary, Thesaurus, Medical, Legal, Financial, Acronyms, Wikipedia.

See also: Formulas for Various Areas (table)Formulas for Various Areas

Plane Figures Area1
triangle ab/2
parallelogram ab
rectangle ab
square s2
circle πr2

Solids Total Surface Area1
right circular cylinder 2π
..... Click the link for more information.

## area,

measure of the size of a surface region, usually expressed in units that are the square of linear units, e.g., square feet or square meters. In elementary geometry, formulas for the areas of the simple plane figures and the surface areas of simple solids are derived from the linear dimensions of these figures. Examples are given in the table entitled Formulas for Various AreasFormulas for Various Areas

Plane Figures Area1
triangle ab/2
parallelogram ab
rectangle ab
square s2
circle πr2

Solids Total Surface Area1
right circular cylinder 2π
..... Click the link for more information.
. The areas of irregular figures, plane or solid, can be computed or closely approximated by the use of integral calculuscalculus,
branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value.
..... Click the link for more information.
.

## Area

a fundamental quantity associated with geometric figures. In the simplest case it is measured by the number of unit squares—that is, squares with sides of unit length—that fill a plane figure.

The calculation of areas was already in antiquity one of the most important problems of practical geometry because of its role in the division of parcels of land. Several centuries before the Common Era, Greek geometers possessed exact rules for the calculation of areas. In Euclid’s Elements these rules were stated in the form of theorems. The areas of polygons were determined by the same methods of decomposition and complementation of figures used today as teaching devices in schools. The areas of figures with curvilinear boundaries were calculated by the method of exhaustion, which, in a certain sense, involved passage to a limit.

The theory of areas of plane figures bounded by simple curves —that is, curves that do not intersect themselves—can be constructed as follows. Let us consider every polygon that can be inscribed in and every polygon that can be circumscribed about a figure F. It should be noted, incidentally, that the area of a polygon can be calculated by calculating the area of an equivalent square obtained by making suitable rectilinear cuts and rearranging the parts obtained. Let {Si} be the number set of areas of the polygons inscribed in the figure, and let {Sd} be the number set of areas of the polygons circumscribed about the figure. [Si] is bounded from above by the area of any circumscribed polygon, and {Sd} is bounded from below by, for example, zero. The least upper bound S̄ of {Si} is called the linear area of F, and the greatest lower bound of {Sd} is the outer area of F. If the inner area of the figure coincides with its outer area, the number S = S̱ – S̄ is called its area, and the figure is said to be squarable (Jordan measurable). A necessary and sufficient condition for a plane figure to be squarable is that for any positive number ∊ there exist a polygon circumscribed about the figure and a polygon inscribed in the figure such that the difference Sd – Si of their areas is less than ∊.

Figure 1

Analytically, the area of a plane figure can be calculated by means of integrals. Suppose F is a curvilinear trapezoid (Figure 1) bounded by the graph of the continuous and nonnegative function f(x) defined on the interval [a, b], by segments of the lines x = a and x = b, and by the segment of the x-axis between the points (a, 0) and (b, 0). The area of the figure can be expressed by the integral

The area of a figure bounded by a closed curve that intersects a line parallel to the y-axis at most twice can be calculated as the difference between the areas of two figures similar to a curvilinear trapezoid. The area of the figure can be expressed in the form of the double integral

S = ∬ dx dy

where the integration extends over the part of the plane occupied by the figure.

The theory of areas of figures on a curved surface can be defined in the following way. Suppose F is a simply connected figure on a smooth surface bounded by a piecewise smooth curve. Let F be partitioned by piecewise smooth curves into a finite

Figure 2

number of parts Φi, each of which has a well-defined projection in the plane tangent to the surface at the point Mi of Φi (Figure 2). Associate to each partition of F the sum of the areas of the projections of all its elements. If for every sequence of partitions of F with diameters approaching zero the corresponding sequence of sums tends to a limit that is independent of the choice of the points Mi, then this limit is defined to be the area of F If F has area, then it is said to be squarable (Jordan measurable). Piecewise smooth, bounded, closed, two-sided surfaces are squarable. The area of a surface is the sum of the areas of its components.

Analytically, the area of a figure F on a surface defined by the equation z = f(x, y), where f is single-valued and has continuous partial derivatives, is given by

Here, G is the closed region that is the projection of F onto the xy-plane, and ds is the element of area of the plane.

### REFERENCES

Fikhtengol’ts, G. M. Kurs differential’nogo i integral’nogo ischisleniia, 7th ed., vol. 2. Moscow, 1969.
Kudriavtsev, L. D. Matematicheskii analiz, vols. 1-2. Moscow, 1970.
Il’in, V. A., and E. G. Pozniak. Osnovy matematicheskogo analiza, 3rd ed., parts 1-2. Moscow, 1971-73.

## area

[′er·ē·ə]
(computer science)
A section of a computer memory assigned by a computer program or by the hardware to hold data of a particular type.
(mathematics)
A measure of the size of a two-dimensional surface, or of a region on such a surface.

## area

1. Measurement of surface within specified boundaries.
2. Space either within or outside a structure or location, designated for a specific purpose, as recreation and/or parking area.
3. An uninterrupted interior space.
4. An areaway.
5. The cross-sectional area of steel reinforcement.

## area

1.
a. the extent of a two-dimensional surface enclosed within a specified boundary or geometric figure
b. the two-dimensional extent of the surface of a solid, or of some part thereof, esp one bounded by a closed curve
2. Anatomy any of the various regions of the cerebral cortex
3. Computing any part of a computer memory assigned to store data of a specified type
References in periodicals archive ?
AUC chairperson Moussa Faki commended Uhuru for taking a leading role in driving Africa's blue economy agenda as well as ensuring the continent harnesses its share of marine resources.
Figure 1 shows the distribution of k, log k, AUC, and log AUC values.
Mean pharmacokinetic parameter of naproxen sodium for marketed immediate release and sustained release tablet (fast, medium and slow) Formulation [T.sub.max] (hr) [C.sub.max] (ug/mL) Immediate release tablet 1.833[+ or -]0.258 54.209[+ or -]10.685 Fast sustained release tablet 2.167[+ or -]0.258 73.767[+ or -]4.889 Medium sustained release tablet 2.667[+ or -]0.258 68.879[+ or -]4.562 Slow sustained release tablet 3.583[+ or -]0.376 63.199[+ or -]3.141 Formulation AUC (hr*ug/mL) Immediate release tablet 147.483[+ or -]36.265 Fast sustained release tablet 307.561[+ or -]7.775 Medium sustained release tablet 391.273[+ or -]82.259 Slow sustained release tablet 391.499[+ or -]69.217 AUC: Area under the curve Table 3.
All the parties to the peace deal, however, formally committed to the establishment of the HCSS "by the AUC to investigate and prosecute individuals bearing criminal responsibility for violations of international law and/or applicable South Sudanese law committed from 15 December 2013 through the end of the transitional period."
Vice President Hurmali reaffirmed the commitment of the GYV to closely work with the AUC towards the two institutions' common goals as well as in the pursuit of the human rights of the African people as provided for in the AUC Strategic Plan and the AU Vision 2063.
"Our partnership with AUC opens new doors for collective action by bringing global solutions for the benefit of Africa to promote economic transformation and development," said the World Bank Group's President.
The meeting discussedTunisia's relations with AUC and means to develop them and also on mechanisms to reinforce the transition process inTunisia, reads a presidency communique.
Both the total and incremental area under the curve (AUC) for free fatty acids after lunch were higher on the no-breakfast days, compared with breakfast days, suggesting that prelunch free fatty acid levels were not the cause of the increased AUC, she said.
A paper, titled "media institutions and the AUC - KUNA experiment," was jointly presented by head of KUNA library section Muna bin Al Ali and secretary of the library Amina Al-Ostath.
HRH the Premier received a letter in regard from AUC Chairperson Dr.
Cairo, Jumada I 12, 1433, Apr 4, 2012, SPA -- The Cultural Attache of the Kingdom of Saudi Arabia in Cairo has supported the Saudi students studying at the American University of Cairo (AUC) and who are participating in the annual festival of the People's Day currently holding in AUC.
A fellow Seventh-day Adventist college has voted not to establish a branch campus at Atlantic Union College (AUC) next semester, as originally planned.

Site: Follow: Share:
Open / Close