Python Program to Check Triangular Number

Posted in Python Tutorial

Updated on Jan 11, 2024

By Mari Selvan

👁️ 119 - Views

⏳ 4 mins

💬 1 Comment

Python Program to Check Triangular Number

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, various mathematical properties of numbers often pique our interest. One such property is whether a number is a triangular number.

A triangular number or triangle number is the sum of the natural numbers up to a certain value.

In this tutorial, we'll delve into a Python program to check if a given number is a triangular number.

📄 Example

Let's explore the Python code that checks whether a given number is a triangular number.

is_triangular_number.py

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import math

# Function to check if a number is a triangular number
def is_triangular_number(num):
    # Formula to check triangular number
    n = int(math.sqrt(2 * num))
    return n * (n + 1) // 2 == num

# Driver program
if __name__ == "__main__":
    # Replace this value with your desired number
    number = 10

    # Check if the number is a triangular number
    if is_triangular_number(number):
        print(f"{number} is a triangular number.")
    else:
        print(f"{number} is not a triangular number.")

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the code.

Output

10 is a triangular number.

Run the script to check if the given number is a triangular number.

🧠 How the Program Works

The program defines a function is_triangular_number that checks if a given number is a triangular number using the formula.
Inside the if __name__ == "__main__": block, replace the value of number with the desired number to check.
The program then calls the is_triangular_number function and prints whether the number is a triangular number or not.

📏 Between the Given Range

Let's take a look at the python code that checks and displays triangular numbers in the range of 1 to 50.

is_triangular.py

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# Function to check if a number is triangular
def is_triangular(num):
    n = 1
    triangular_number = 1

    while triangular_number < num:
        n += 1
        triangular_number = n * (n + 1) // 2

    return triangular_number == num

# Display triangular numbers in the range 1 to 50
def display_triangular_numbers():
    lower_limit = 1
    upper_limit = 50

    print(f"Triangular Numbers in the Range {lower_limit} to {upper_limit}:")

    for num in range(lower_limit, upper_limit + 1):
        if is_triangular(num):
            print(num, end=" ")

# Call the function to display triangular numbers
display_triangular_numbers()

💻 Testing the Program

Output

Triangular Numbers in the Range 1 to 50:
1 3 6 10 15 21 28 36 45

Run the script to see the triangular numbers in the specified range.

🧠 How the Program Works

The program defines a function is_triangular that checks if a given number is a triangular number.
Inside the function, it uses a while loop to find the smallest triangular number greater than or equal to the given number.
The display_triangular_numbers function iterates through the range 1 to 50, calling is_triangular for each number and printing the triangular numbers.

🧐 Understanding the Concept of Triangular Numbers

Before delving into the code, let's take a moment to understand the concept of triangular numbers.

A triangular number is the sum of the natural numbers up to a certain value, and it can be represented by the formula T_n = n * (n + 1) / 2, where n is a non-negative integer.

For example, T₃ = 1 + 2 + 3 = 6 is a triangular number.