Worlds of David Darling
Encyclopedia of Science
   
Home > Encyclopedia of Science

intersection





A place where two or more things meet or overlap. Two lines or curves intersect at a point, two planes can intersect in a line, and so forth. The intersection of two or more sets , represented by cap symbol, is the set of elements that all the sets have in common; in other words, all the elements contained in every one of the sets.

In plane geometry, an intersection is the crossing of two lines or curves at a point known as the point of intersection. In terms of analytic geometry, if two lines have equations y = f(x) and y = g(x) where f(x) and g(x) are functions of x, their points of intersection are given by those values of x for which f(x) = g(x). For example, the line y = 2x intersects the curve y = x2 in two points whose coordinates are given by solution of the equation 2x = x2; this has two roots, 0 and 2, and hence the points of intersection are (0,0) and (2,4). Should the equation f(x) = g(x) have roots that are not unique (i.e., two or more are equal), then the curves are tangential at the point or points defined by the equal roots.


Related category

   • MATHEMATICAL TERMINOLOGY