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: 2,150 Thanks: 730 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: 14,326 Thanks: 1023 
2 with integer areas: 131415 , area 84 515253, 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 n1, 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: 6,730 Thanks: 689 
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 
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  
June 4th, 2014, 12:27 PM  #8 
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689  

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