The formula of the distance between two straight lines is: let the equation of two straight lines be Ax+By+C 1=0, Ax+By+C2=0. The distance from p to the straight line Ax+By+C2=0 is d = | AA+BB+C2 |/√ (A2+B2) = |-c1+C2 |/√ (A2+B2) = | c1-C2 |/.
Distance introduction:
In mathematics, distance is one of the most basic concepts in functional analysis. The distance space defined by it connects topological space with normed linear space and other spaces, and it is the first contact concept of learning functional analysis. Distance refers to the length of a straight line between any two points.
Function introduction:
Functional is an important basic concept in mathematics, one of the important research objects of modern mathematics and an important tool for research and application in mathematics and other fields. Functional analysis is a branch of studying the mapping from topological linear space to topological linear space satisfying various topological and algebraic conditions.
It was founded in the 1930s. It is developed from the study of variational method, differential equation, integral equation, function theory and quantum physics. It can be regarded as infinite dimensional analysis by using the viewpoints and methods of geometry and algebra.
Let {y} be a given set of functions. If there is always a certain number in this set of functions corresponding to any function y(x), it is denoted as п (y (x)), then п (y (x)) is a functional defined on the set {y(x)}. The function in the function definition domain is expected function or allowed function, and y(x) is called the variable function of functional п.
The functional п (y(x)) has a clear correspondence with the expected function y(x). The value of the functional is determined by the overall properties of the required curve. Functional is also a kind of "function", and its independent variable is generally not the "independent variable" of ordinary function, but the ordinary function itself. A functional is a function of a function.
Because the function value is determined by the choice of independent variables, and the value of functional is determined by the function of independent variables, it can also be understood as the function of function. The independent variable of functional is function, and the independent variable of functional is called independent variable. In short, a functional is a function of a function.