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Q: What is the total of the decreases of a triangles?
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How many degrees total the degrees total the sum of any triangles?

There are 180 degrees in any and all triangles.


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What is the recurrence relation of the number of triangles inside a triangle?

Well, it just so happens that I figured this out for whoever was wondering... When n is even, and n+1 is odd (obviously) Sn+1 = Sn + (n+2)(3n+2)/4 When n is odd, and n+1 is even (obviously) Sn+1 = Sn + (n+1)(3n+5)/4 These formulas are for the total triangles in something that looks like this... /\ /_\ /\ /\ /_\ /_\ /\ /\ /\ /_\ /_\ /_\ This triangle has n=3 and has 13 total triangles. The general formula for total triangles is hard to find. And because this question doesn't ask for the general solution for any n, I won't post it. It is really fun to find though... The solution is shown below... Total Number of triangles = (n*n) + ( (n) * (n-1) * (4n+1) / 2 ) where n = (k+1) /2. K is the number of triangles on the each side. In the above example k is 3. k = 1 -> Total Triangles = 1 k = 2 -> Total Triangles = 4.875 ~ 5 k = 3 -> Total Triangles = 13 k = 4 -> Total Triangles = 26.875 ~ 27 k = 5 -> Total Triangles = 48 k = 6 -> Total Triangles = 77.875 ~ 78 and so on....


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