Polygon Diagonal FormulaDate: 8/20/96 at 0:26:41 From: Myer Moses Subject: Use of Polygon Diagonal Formula I know the formula for the number of diagonals in a polygon is d = [s(s - 3)]/2. Does this same formula apply to other parts of geometry? Date: 8/20/96 at 11:2:29 From: Doctor Anthony Subject: Re: Use of Polygon Diagonal Formula For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals. So the total number of diagonals that can be drawn is n(n-3). However this method means that each diagonal will be drawn twice, (to and from each vertex), so the expression must be divided by 2, to give: number of diagonals of polygon = n(n-3)/2 You can see that the formula arises from the nature of the diagram and the construction of the diagonals. There is no reason why this formula should fit any other property of polygons, like the number of triangles formed when you draw in the diagonals. Each of these questions must be reasoned out on its own merits. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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