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The mathematics of ancient Mesopotamia, Egypt, and Greece had no explicit concept of negative numbers or signed areas, but had notions of shapes contained by some boundary lines or curves, whose areas could be computed or compared by pasting shapes together or cutting portions away, amounting to addition or subtraction of areas. [1]
A net = is said to be frequently or cofinally in if for every there exists some such that and . [5] A point is said to be an accumulation point or cluster point of a net if for every neighborhood of , the net is frequently/cofinally in . [5] In fact, is a cluster point if and only if it has a subnet that converges to . [6] The set of all ...
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 net has to be such that the straight line is fully within it, and one may have to consider several nets to see which gives the shortest path. For example, in the case of a cube , if the points are on adjacent faces one candidate for the shortest path is the path crossing the common edge; the shortest path of this kind is found using a net ...
Table of Shapes Section Sub-Section Sup-Section Name Algebraic Curves ¿ Curves ¿ Curves: Cubic Plane Curve: Quartic Plane Curve: Rational Curves: Degree 2: Conic Section(s) Unit Circle: Unit Hyperbola: Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de Sluze: Right Strophoid: Semicubical Parabola: Serpentine Curve: Trident ...
± (plus–minus sign) 1. Denotes either a plus sign or a minus sign. 2. Denotes the range of values that a measured quantity may have; for example, 10 ± 2 denotes an unknown value that lies between 8 and 12. ∓ (minus-plus sign) Used paired with ±, denotes the opposite sign; that is, + if ± is –, and – if ± is +.
A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles.
The vector area of a surface can be interpreted as the (signed) projected area or "shadow" of the surface in the plane in which it is greatest; its direction is given by that plane's normal. For a curved or faceted (i.e. non-planar) surface, the vector area is smaller in magnitude than the actual surface area.