document.write( "Question 194454: I don't understand Euler's Law, v+f=e+2
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Algebra.Com's Answer #145938 by Edwin McCravy(20056) $\"\"$ $\"About$

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I don't understand Euler's Law, v+f=e+2\r
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document.write( "Euler's formula holds for every solid figure consisting of\r\n" );
document.write( "vertices, flat faces, and straight edges.\r\n" );
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document.write( "For any solid figure with only flat surfaces and \r\n" );
document.write( "straight edges, this formula always holds:\r\n" );
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document.write( "Number of vertices + number of faces = number of edges + 2\r\n" );
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document.write( "Here is a demonstration of that formula with a \"box\",\r\n" );
document.write( "that is, a rectangular solid:\r\n" );
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document.write( "Count the vertices (sharp corners).  They are \r\n" );
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document.write( "A, B, C, D, E, F, G, H\r\n" );
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document.write( "That's 8.  So for the above figure, v = 8\r\n" );
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document.write( "-----\r\n" );
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document.write( "Count the faces (flat surfaces).  They are rectangles \r\n" );
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document.write( "ABCD, EFGH, AEHD, BFGC, ABFE, DCGH, \r\n" );
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document.write( "That's 6.  So for the above figure, f = 6\r\n" );
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document.write( "-----\r\n" );
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document.write( "Count the edges.  They are line segments: \r\n" );
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document.write( "AB, BC, CD, DA, EF, FG, GH, HE, AE, BF, DH, CG\r\n" );
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document.write( "That's 12.  So for the above figure, e = 12\r\n" );
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document.write( "-----\r\n" );
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document.write( "Now look at Euler's formula:\r\n" );
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document.write( "Substituting,\r\n" );
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document.write( "So you see that Euler's formula holds for the\r\n" );
document.write( "above rectangular solid.\r\n" );
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document.write( "Euler's formula holds for every solid figure consisting of\r\n" );
document.write( "vertices, flat faces, and straight edges.\r\n" );
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document.write( "Edwin

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