Answer by Sven Marnach for Checking if float is equivalent to an integer value in python

Both your implementations have problems. It actually can happen that you end up with something like 4.999999999999997, so using int() is not an option.

I'd go for a completely different approach: First assume that your number is triangular, and compute what n would be in that case. In that first step, you can round generously, since it's only necessary to get the result right if the number actually is triangular. Next, compute n * (n + 1) / 2 for this n, and compare the result to x. Now, you are comparing two integers, so there are no inaccuracies left.

The computation of n can be simplified by expanding

(1/2) * (math.sqrt(8*x+1)-1) = math.sqrt(2 * x + 0.25) - 0.5

and utilizing that

round(y - 0.5) = int(y)

for positive y.

def is_triangular(x):    n = int(math.sqrt(2 * x))    return x == n * (n + 1) / 2