How to Name a Polygon by VerticesDate: 06/30/2004 at 19:26:23 From: Claudia Subject: variable naming convention Is there a specific convention for naming the vertices of polygons? For example, picture a triangle with vertices at R (0, 0), S (0, 3), and T (4, 0). Would you call this triangle RST or RTS? In other words, is the figure named by going clockwise or counter- clockwise? How do you determine the first vertex named? Are there ever exceptions? Date: 06/30/2004 at 23:06:50 From: Doctor Peterson Subject: Re: variable naming convention Hi, Claudia. A triangle can be named in any order at all; a polygon in general can be named by starting at any point and going either clockwise or counterclockwise. There is good reason for this. In many cases we don't care about the direction or the starting point; it makes no difference in most theorems. Usually we don't even know the direction of the points; that is not one of the facts given in the statement of the theorem. And perhaps most important, we need to be able to say in a figure like this A /|\ / | \ / | \ / | \ / | \ C-----B-----D that triangles ABC and ABD are congruent; but if we had to name triangles in a certain order, then one of these two names would be illegal, since if one is clockwise then the other has to be counterclockwise! So don't worry about consistency. In fact, if you are teaching, you should deliberately name triangles in different orders, to get students used to the fact that naming does not imply anything about orientation. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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