Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: definition of parallel lines



"Frohne, Vickie" wrote:

In
plane geometry, ... there exists only one line
through a specified point that
is parallel to a given line.

True, but not a definition.

... surface of a globe, ... There are NO parallel lines
in this space. Every pair of great circles will intersect.

Evidently taking non-intersection to be the definition
of parallel.

That is one possible definition, but not the only possible
definition. According to my dictionary, possibilities include
a) non-intersection
b) everywhere equidistant
c) locally equidistant
d) common perpendiculars

... all of which are equivalent in flat space.

Note (c) and (d) hinge on _local_ properties and hence are
favored by physicists. These also agree with vernacular
usage, and are best in tune with the question that started
this thread.

Note that the well-known "parallels" of lattitude are
equidistant (but not straight) "lines".