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:
“I find nothing healthful or exalting in the smooth conventions of society. I do not like the close air of saloons. I begin to suspect myself to be a prisoner, though treated with all this courtesy and luxury. I pay a destructive tax in my conformity.”
—Ralph Waldo Emerson (1803–1882)