TITLE: Is there a difference between a geometric shape and a geometric figure?
QUESTION [12 upvotes]: Many writers seem to use the words "Shape" and "Figure" interchangeably, and few give definitions of these terms. Is there a difference, and if so what is it ?

REPLY [7 votes]: There are nuances one might want to distinguish between here (for example whether a different scale, orientation or position makes something into a different figure/shape), but there is no widespread and generally understood convention for how to make those distinction with a choice between "shape" and "figure".
As a writer, you should not depend on a reader understanding such differences from your choice of words, so if you need to make the distinction, you'll need to explain explicitly how you use each word.
As a reader, be extremely wary of assuming that an author is using the words with any particular distinction in mind, unless he explicitly explains that he is. At worst, you may need to reconstruct the particular definitions the author is using such that what he says makes sense.