Question

A continuous arc without multiple points is called a​

Answer 1

In general, given any y=f(x), we can think of this as the vector function r(t)=⟨t,f(t),0⟩. Then r′(t)=⟨1,f′(t),0⟩ and |r′(t)|=√1+(f′)2. The length of the curve y=f(x) between a and b is thus ∫ba√1+(f′(x))2dx.

Answer 2

Such an arc is known as the Jordan arc.

• An injective continuous map of a closed and bounded interval [a, b] into the principal plane is the image of such a recurring arc in the plane.
• It in common is a plane curve that's neither smooth nor of algebra nature by standard definition.
• The arc f is frequently described as an injection path, with the beginning point of f differing from the ultimate position of f.