PHP Program to Check Triangular Number

Posted in PHP Tutorial

Updated on Oct 31, 2024

By Mari Selvan

👁️ 58 - Views

⏳ 4 mins

💬 1 Comment

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 PHP program to check if a given number is a triangular number.

📄 Example

Let's delve into the PHP code that checks whether a given number is a triangular number.

isTriangularNumber.php

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<?php
// Function to check if a number is a triangular number
function isTriangularNumber($num)
{
  // Formula to check triangular number
  $n = (int)sqrt(2 * $num);
  return ($n * ($n + 1)) / 2 == $num;
}

// Replace this value with your desired number
$number = 10;

// Check if the number is a triangular number
if (isTriangularNumber($number))
{
  echo "$number is a triangular number.\n";
}
else
{
  echo "$number is not a triangular number.\n";
}

?>

💻 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 isTriangularNumber that checks if a given number is a triangular number using the formula.
Replace the value of $number with the desired number to check.
The program then calls the isTriangularNumber function and prints whether the number is a triangular number or not.

📏 Between the Given Range

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

isTriangular.php

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<?php
// Function to check if a number is triangular
function isTriangular($num)
{
  $sum = 0;
  $i = 1;

  // Keep adding natural numbers to the sum until it exceeds or equals $num
  while ($sum < $num)
  {
    $sum += $i;
    $i++;
  }

  // Check if the sum equals $num
  return $sum == $num;
}

// Display triangular numbers in the range 1 to 50
echo "Triangular Numbers in the Range 1 to 50:\n";

for ($i = 1;$i <= 50;$i++)
{
  if (isTriangular($i))
  {
    echo "$i ";
  }
}

?>

💻 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 range from 1 to 50.

🧠 How the Program Works

The program defines a function isTriangular that checks if a given number is triangular using the triangular number formula.
Inside the main section, a loop iterates through numbers from 1 to 50.
For each number, the program checks if it is triangular using the isTriangular function.
Triangular numbers in the specified range are displayed in the desired format.

🧐 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.