Dissecting a Square into Acute TrianglesDate: 11/09/1999 at 11:26:31 From: Adam Sheraden Subject: Geometry Can you dissect a square into a finite number (fewer than 14) of acute triangles? Date: 11/09/1999 at 13:07:06 From: Doctor Rob Subject: Re: Geometry Thanks for writing to Ask Dr. Math, Adam. Put the vertices of the square at A(0,0), B(10,0), C(10,10), and D(0,10). Mark points along the sides at E(5,0), F(10,6), G(5,10), and H(0,6). Mark points in the interior at I(3,4), J(7,4), K(6,7), and L(4,7). Then connect AI, BJ, CK, DL, EI, EJ, FJ, FK, GKJ, GLI, HI, and HL. Prove that GKJ and GLI are straight lines. Then prove that the 12 triangles formed are all acute. For just 8 triangles, see the top of David Eppstein's page from the Geometry Junkyard, Triangles and Simplices: http://www1.ics.uci.edu/~eppstein/junkyard/triangulation.html - Doctors Rob and Schwa, The Math Forum http://mathforum.org/dr.math/ |
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