Triangular number verifier (Python)

#! /usr/bin/env python3

the_number = 1000000000000

def is_triangular_number_formula(number):
    root_of_square = (number * 8 + 1) ** 0.5
    return root_of_square == round(root_of_square)

# print(is_triangular_number_formula(the_number))
# 6 function calls in 0.000 seconds

def is_triangular_number_algorithm_one(number):
    accumulator = 0
    counter = 0

    while accumulator <= number:
        accumulator += counter
        counter += 1

        if accumulator == number:
            result = True
            break
    else:
        result = False

    return result

# print(is_triangular_number_algorithm_one(the_number))
# 5 function calls in 0.474 seconds

def is_triangular_number_algorithm_two(number):
    counter = 0

    if number == 0:
        return True

    while number > 0:
        counter += 1
        number -= counter

        if number == 0:
            result = True
            break
    else:
        result = False

    return result

# print(is_triangular_number_algorithm_two(the_number))
# 5 function calls in 0.419 seconds

def is_triangular_number_algorithm_three(number):
    for counter in range(number + 1):
        triangular_number = counter * (counter + 1) // 2
        if number == triangular_number:
            return True
        if number < triangular_number:
            return False

# print(is_triangular_number_algorithm_three(the_number))
# 5 function calls in 0.679 seconds