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 June 3rd, 2014, 04:32 AM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 sequential ABC is triangle the sides is sequential series find it
 June 3rd, 2014, 04:49 AM #2 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions uh... 3:4:5?
 June 3rd, 2014, 06:55 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 2 with integer areas: 13-14-15 , area 84 51-52-53, area 1170
 June 3rd, 2014, 06:57 AM #4 Senior Member     Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry There are infinite number of such triangles. Such as, the edges of triangle are $\displaystyle x, \; x+ \alpha , \; a+ 2 \alpha$. Are lengths of edges integers, what type of sequence is it, and etc.?
 June 3rd, 2014, 08:41 AM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Let m > 0 be an integer and n = $(2+\sqrt3)^m+(2-\sqrt3)^m.$ Then n is an integer and n-1, n, n+1 are the sides of a triangle with integer area.
 June 3rd, 2014, 02:44 PM #6 Global Moderator   Joined: May 2007 Posts: 6,805 Thanks: 716 Any 3 integers will do as long as the sum of any two is greater than the third.
June 3rd, 2014, 09:35 PM   #7
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Quote:
 Originally Posted by mathman Any 3 integers will do as long as the sum of any two is greater than the third.
I can only assume this question is a sort of Rorschach test to see who sees the problem in what ways.

June 4th, 2014, 12:27 PM   #8
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Quote:
 Originally Posted by CRGreathouse I can only assume this question is a sort of Rorschach test to see who sees the problem in what ways.
You could be right. I am not a mind reader.

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