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What is a simple curve & a non simple curve?
What are the elements of a simple curve?
Is a curve a line or a shape?
What is the difference between a closed curve and a simple curve?
Both simple and non-simple curves can be open or closed but a simple curve does not cross itself whereas a non-simple curve crosses its own path at least once.
A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it. For example, a circle is an example of curved-shape. In Mathematics, Geometry is a branch that deals with shapes, sizes, and the properties of figures. Geometry can be classified into two types.
All we need is geometry plus names of all elements in simple curve. Note that we are only dealing with circular arc, it is in our great advantage if we deal it at geometry level rather than memorize these formulas.
A simple curve can be represented mathematically by a continuous function that has no self-intersections. Every simple closed curve can be continuously deformed into a circle without breaking or overlapping.
A simple curve is a continuous, non-self-intersecting path in a two-dimensional or three-dimensional space. It is a fundamental concept in vector calculus, particularly in the context of conservative vector fields.
A parabola, one of the simplest curves, after (straight) lines. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.
It should be noted that for a given intersecting angle or central angle, when using the arc definition, all the elements of the curve are inversely proportioned to the degree of curve. This definition is primarily used by civilian engineers in highway construction.
