Complement
In general, the word "complement" refers to that subset 
of some set 
which excludes a given subset 
. Taking 
and its complement 
together then gives the whole of the original set. The notations
and 
are commonly used to denote the complement of a set 
.
This concept is commonly used and made precise in the particular cases of a complement point, graph complement, knot complement, and complement set. The word "complementary" is also used in the same way, so combining an angle and its complementary angle gives a right angle and a complementary error function erfc and the usual error function erf give unity when added together,
 |
(1) |
The complement point of a point 
with respect to a reference
triangle 
,
also called the inferior point, subordinate point, or medial image, is the point
such that
 |
(2) |
where 
is the triangle centroid.
The complement point of a point with trilinear coordinates 
is therefore given by
 |
(3) |
The following table lists the complements of some named circles.
The complement of a line
 |
(4) |
is given by the line
 |
(5) |
The following table summarizes the complements of a number of named lines.
The following table summarizes the complements of several common triangle centers.
See also
Anticomplement, Complement Set, Complementary Angles, Erfc, Graph Complement, Homothecy, Homothetic Center, Knot Complement, Similitude Ratio, Triangle Centroid
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References
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, p. 23, 1984.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Complement." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Complement.html