curve
Generally it is the bent line where the curve (curve) is not honest, a word it wants to do it, and to mean the line which is not a straight line.
In the mathematics, I include a straight line and a concept for the line in a curve as the special case.
In analytic geometry in particular, the curve is described essentially with the group of the continuous function of the number of the complete changes.
Parameter t section I (for example, whole number line R or closed interval) with real number[0, 1] Shall move in continuous function φ(t),ψ(t) I give を.
It is x =φ(t), y =ψ then(t) By a far-off thing in xy- plane R,(x, y) = (φ(t),ψ(t)) The trace of a point shown で to is called a plane curve.
Or it is φ in this(t) = (φ(t),ψ(t)) Real variable vector function φ which I put and is provided: I can call I → R itself a plane curve.
A curve gets a direction from big things and small things relations in I naturally then.
It is x =φ(t) But, if can untie it about t; t =φ(x) Can write and y =ψ(φ(x)) continuous function f are provided.
On the contrary, there is continuous function f; and y = f(x) If if can write と, put it with φ= idI,ψ= f (but or is the same thing, x = t, y = f(t)); (φ(t),ψ(t)) = (x, f(x)) The trace draws a plane curve.
Or it is x =φ(t), y =ψ(t) If を is alliance, and can erase parameter t, it uses continuous function F of two variables; and F(x, y) = 0 form can express it.
Generally F = 0 includes plural implicit functions as well as an original curve then.
Even if a level of the space rises as for having looked at the top, the same thing can say essentially.
Generally I write down the case of the n dimension.
Family x of the point in R touched an additional character in parameter t changing in a certain section I continually(t) = (x1(t), x2(t),... xn(t)) Each で xk(t) But, thing trace becoming the continuous function about t or function x: I call I → R itself a curve in the n dimension space.
I call time of n = 3 space curve in particular.
For general topological space E, I say an image of consecutive representation ρ defined on section I or representation itself with a curve in E likewise.
In the mathematics, I include a straight line and a concept for the line in a curve as the special case.
In analytic geometry in particular, the curve is described essentially with the group of the continuous function of the number of the complete changes.
Parameter t section I (for example, whole number line R or closed interval) with real number[0, 1] Shall move in continuous function φ(t),ψ(t) I give を.
It is x =φ(t), y =ψ then(t) By a far-off thing in xy- plane R,(x, y) = (φ(t),ψ(t)) The trace of a point shown で to is called a plane curve.
Or it is φ in this(t) = (φ(t),ψ(t)) Real variable vector function φ which I put and is provided: I can call I → R itself a plane curve.
A curve gets a direction from big things and small things relations in I naturally then.
It is x =φ(t) But, if can untie it about t; t =φ(x) Can write and y =ψ(φ(x)) continuous function f are provided.
On the contrary, there is continuous function f; and y = f(x) If if can write と, put it with φ= idI,ψ= f (but or is the same thing, x = t, y = f(t)); (φ(t),ψ(t)) = (x, f(x)) The trace draws a plane curve.
Or it is x =φ(t), y =ψ(t) If を is alliance, and can erase parameter t, it uses continuous function F of two variables; and F(x, y) = 0 form can express it.
Generally F = 0 includes plural implicit functions as well as an original curve then.
Even if a level of the space rises as for having looked at the top, the same thing can say essentially.
Generally I write down the case of the n dimension.
Family x of the point in R touched an additional character in parameter t changing in a certain section I continually(t) = (x1(t), x2(t),... xn(t)) Each で xk(t) But, thing trace becoming the continuous function about t or function x: I call I → R itself a curve in the n dimension space.
I call time of n = 3 space curve in particular.
For general topological space E, I say an image of consecutive representation ρ defined on section I or representation itself with a curve in E likewise.