Kata

Description:

A triangle number is a number where n objects form an equilateral triangle (it's a bit hard to explain). For example, 6 is a triangle number because you can arrange 6 objects into an equilateral triangle:

  1
 2 3
4 5 6

8 is not a triangle number because 8 objects do not form an equilateral triangle:

   1
  2 3
 4 5 6
7 8

In other words, the nth triangle number is equal to the sum of the n natural numbers from 1 to n.

Your task:

Check if a given input is a valid triangle number. Return true if it is, false if it is not (note that any non-integers, including non-number types, are not triangle numbers).

You are encouraged to develop an effective algorithm: test cases include really big numbers.

Assumptions:

You may assume that the given input, if it is a number, is always positive.

Notes:

0 and 1 are triangle numbers.