11 Facts About Space curve

In mathematics, a Space curve is an object similar to a line, but that does not have to be straight.

Plane algebraic Space curve is the zero set of a polynomial in two indeterminates.

Since the nineteenth century, Space curve theory is viewed as the special case of dimension one of the theory of manifolds and algebraic varieties.

Topological curve can be specified by a continuous function from an interval of the real numbers into a topological space.

In other words, if a Space curve is defined by a continuous function with an interval as a domain, the Space curve is simple if and only if any two different points of the interval have different images, except, possibly, if the points are the endpoints of the interval.

Intuitively, a simple Space curve is a Space curve that "does not cross itself and has no missing points" .

The image of a simple curve can cover a square in the plane and thus have a positive area.

For example, a fractal Space curve can have a Hausdorff dimension bigger than one and even a positive area.

Roughly speaking a differentiable Space curve is a Space curve that is defined as being locally the image of an injective differentiable function from an interval of the real numbers into a differentiable manifold, often.

In other words, a differentiable Space curve is a differentiable manifold of dimension one.

The whole Space curve, that is the set of its complex point is, from the topological point of view a surface.