Conventions and Terminology
The distinction between a curve and its image is important. Two distinct curves may have the same image. For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times. Many times, however, we are just interested in the image of the curve. It is important to pay attention to context and convention in reading.
Terminology is also not uniform. Often, topologists use the term "path" for what we are calling a curve, and "curve" for what we are calling the image of a curve. The term "curve" is more common in vector calculus and differential geometry.
Read more about this topic: Curve
Famous quotes containing the word conventions:
“Why does almost everything seem to me like its own parody? Why must I think that almost all, no, all the methods and conventions of art today are good for parody only?”
—Thomas Mann (1875–1955)