kini.Amith said:Is a curve (Say 'S') 1d or 2d? I ask this question because for so long i was under the impression that it was 2d, since we need a 2d cartesian plane to draw and describe a curve. But then i read in a popular book that it was 1D, which is hard to believe. so which is it?
Lets say the curve is positively sloped. If you move forward (to the right), you would also be moving 'up'. Doesnt that means its 2D?Landau said:Intuitively: imagine living on a curve (forgetting about the "embedding", thinking of the curve as everything there is), then you can only go forward or backwards, i.e. moving along the curve. Phycisists would say something like "there is only one degree of freedom".
Curve S is a mathematical curve that is often studied in geometry and calculus. It is important to explore its dimensions because it can provide insights into the behavior of other curves and surfaces in higher dimensions.
This is a debated question among mathematicians. Some argue that Curve S is one-dimensional because it can be described by a single parameter, while others argue that it is two-dimensional because it exists in a two-dimensional space.
Techniques such as parametric equations, polar coordinates, and vector calculus are commonly used to study the dimensions of Curve S. Computer software and visualizations are also helpful tools in understanding its properties.
The dimensions of Curve S have a significant impact on its curvature. In one-dimensional space, the curvature of Curve S is constant, while in two-dimensional space, it can vary based on the direction in which it is measured.
Yes, Curve S can be extended into higher dimensions, such as 3D or even n-dimensional space. However, it becomes increasingly difficult to visualize and analyze its properties as the dimensions increase.