May 23rd, 2012, 11:57 AM  #11  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Paper problem Quote:
Edit: In fact it is possible in some cases, depending on how you interpret "isosceles". Consider a right triangle with sides of length 2, and 1, and bisect the side of length 2 through the opposite vertex. The resulting triangles have sides with lengths 1, and 1; 1, 1, and 1.  
May 23rd, 2012, 01:32 PM  #12 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  Re: Paper problem
ok, take any rightangled triangle. Complete it to make a rectangle. One of the sides of the original triangle is a diagonal of that rectangle. Now draw the other diagonal. Do you agree that the two diagonals cut the rectangle in 4 isosceles triangles? and that two of these isosceles triangles belong to the original rightangled triangle? is that a number theoretic question by the way? 
May 23rd, 2012, 02:19 PM  #13  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond  Re: Paper problem Quote:
 
May 23rd, 2012, 03:04 PM  #14  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Paper problem Quote:
 
May 24th, 2012, 12:05 AM  #15 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  Re: Paper problem
there is also a dissection of some scalene triangles into 3 isosceles triangles. But it doesn't work for any triangle. Take a triangle ABC and consider the center D of the circle containing its three vertices. If this point lies inside the triangle, then draw a line from D to each of A,B,C. The three triangles ABD, BCD and CAD are isosceles. In the case of a right angle triange D lies on one side and there are only two triangle (plus a flat triangle).


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