Fastest method to define whether a number is a triangular number

Question

A triangular number is the sum of the n natural numbers from 1 to n. What is the fastest method to find whether a given positive integer number is a triangular one?

He

Answer 1

   int tri=(8*number)+1;// you can remove this for checking the perfect square and remaining all same for finding perfect square
   double trinum=Math.sqrt(tri);
int triround=(int) Math.ceil(trinum);
if((triround*triround)==tri)
     {
     System.out.println("Triangular");
     }
    else
    {
    System.out.println("Not Triangular");
    }

Here ceil will always look at next highest number so this will give a perfect chance for verification.