The problem of multivariate function in advanced mathematics, I'm a little confused about the definition of n-dimensional space, because I think three-dimensional solid, what more? Moreover, binary function is a surface, which is a solid, and what graph is the function with more than two variables? When talking about the curve integral of arc length, in the definition, f (x, y) is an integrand function, But shouldn't an arc be a function of one variable? How can it be a function of two variables? It's an integrand. I think I'm completely confused by the concept,

The problem of multivariate function in advanced mathematics, I'm a little confused about the definition of n-dimensional space, because I think three-dimensional solid, what more? Moreover, binary function is a surface, which is a solid, and what graph is the function with more than two variables? When talking about the curve integral of arc length, in the definition, f (x, y) is an integrand function, But shouldn't an arc be a function of one variable? How can it be a function of two variables? It's an integrand. I think I'm completely confused by the concept,

Beyond three dimensions are hyperplanes and hypersurfaces. Only theoretical research value can be found, and it is impossible to find the contrast in reality
A binary equation f (x, y) = 0 represents a straight line or curve in the plane coordinate system, and a ternary equation f (x, y, z) = 0 represents a plane or surface in the space coordinate system
According to the physical meaning of the curve integral of the arc length, the integrand function represents the linear density of the curve. For example, the linear density of the plane curve is of course a binary function. If the curve equation is substituted, it will eventually become a unary function. Isn't that the idea of calculating the curve integral