Reverse Triangle Number Algorithm

**sphynx01** · 12-24-2014, 04:41 AM

Hi, can anyone help me reverse the Triangle Number algorithm please? The Triangle Number algorithm is A1*(A1+1)/2. This returns a cumulative result of 1, 3, 6, 10, 15, 21, etc...

I need to reverse this... I have the number 21 and need to get the number 6 out of it (without a long string of if-then statements of course). Obviously the easiest way is to make it a Square Number first (and get the square root), so have to make that 21 a 36 first with the same algorithm that makes the 15 into a 25. At least, that seems the most obvious way... :/

**sphynx01** · 12-24-2014, 04:55 AM

I should comment that I'm currently using this algorithm, though it comes up with the right results, it only does so due to the rounding down as it generally returns a result of about 0.48 over the actual number.

=ROUNDDOWN(SQRT(A1*2),0)

**MrShorty** · 12-24-2014, 10:14 AM

Would you be willing to go all the way back to your algebra class and recall how to use the quadratic formula to solve 2nd degree polynomials: http://www.purplemath.com/modules/quadform2.htm The first example in this link should look very close to the kind of problem you have here.

Wikipedia describes an equation for finding the "triangular root" of a number: http://en.wikipedia.org/wiki/Triangle_numbers