optical path = μ x geometricalpath
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A base path is the path determined by the runner as he is travelling between bases, and the base line is the the direct lines between the two bases.
absolute path is an exact road to go in and path is just a relative path, for example the path is near the river - for a path and for an absolute path you can say the path is on green lake street on the intersection of green lake street and Burnside street.
One measure of distance between them.
The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.
Yes, they can exist.