document.write( "Question 637939: The possible triangulations T(n) of an n-gon, for n = 3, 4, and 5
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\n" ); document.write( "T(3) = 1 (A triangle is its own triangulation)
\n" ); document.write( "T(4) = 2 (A convex quadrilateral can be triangulated diagonally on each of two diagonals)
\n" ); document.write( "T(5)= 5 ((A pentagon can be triangulated with two segments joining each vertex to its two opposite vertices)\r
\n" ); document.write( "\n" ); document.write( "Determine T(n) for n = 6, 7, and 8
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Algebra.Com's Answer #401977 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'm not sure how it works or how it's derived entirely, but the formula for triangulating any n-gon (n is an integer and n >= 3) is\r
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document.write( "Pickover, Clifford A. \"Euler's Polygon Division Problem.\" The Math Book: From\r\n" );
document.write( "       Pythagoras to the 57th Dimension, 250 Milestones in the History of \r\n" );
document.write( "       Mathematics. New York, NY: Sterling Pub., 2009. 184. Print.\r\n" );
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document.write( "More Source Info: \r\n" );
document.write( "                  Formula found in page 184 of this book. \r\n" );
document.write( "                  See this page (page 184) in google books here so you can see the formula for yourself.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In the case of a triangle, T(3) = (2)/(3-1)! = 2/2 = 1, which means that there is only one way to triangulate a triangle.\r
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\n" ); document.write( "\n" ); document.write( "In the case of a quadrilateral, T(4) = (2*6)/(4-1)! = 12/6 = 2, which means that there are two ways to triangulate a quadrilateral.\r
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\n" ); document.write( "\n" ); document.write( "In the case of a pentagon, T(5) = (2*6*10)/(5-1)! = 120/24 = 5, which means that there are 5 ways to triangulate a pentagon.\r
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\n" ); document.write( "\n" ); document.write( "In the case of a hexagon, T(6) = (2*6*10*14)/(6-1)! = 1680/120 = 14, which means that there are 14 ways to triangulate a hexagon.\r
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\n" ); document.write( "\n" ); document.write( "You continue this pattern to find the triangulation for any convex n-gon. \n" ); document.write( "
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