**π‘ Problem Formulation:** We often encounter geometrical problems in programming that require validation of shapes based on their properties. In a triangle, a fundamental rule is that the sum of any two sides must be greater than the third. This article explores five methods to check the validity of a triangle in Python when the lengths of the sides are provided. For instance, given side lengths 3, 4, and 5, the program should indicate that it forms a valid triangle.

## Method 1: Using Basic Conditional Statements

This traditional approach employs simple conditional checks to validate the triangle’s existence by ensuring the sum of any two sides is greater than the remaining one.

Here’s an example:

def is_valid_triangle(a, b, c): if (a + b > c) and (a + c > b) and (b + c > a): return True else: return False print(is_valid_triangle(3, 4, 5))

Output: True

This function `is_valid_triangle()`

takes three arguments representing the sides of a triangle and returns `True`

if they satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. The output confirms that sides of lengths 3, 4, and 5 can form a valid triangle.

## Method 2: Using the Sort and Compare Technique

This method involves sorting the sides in ascending order to make the comparison logic simpler and clearer. The largest side is compared to the sum of the other two to check the validity of a triangle.

Here’s an example:

def is_valid_triangle(a, b, c): sides = sorted([a, b, c]) return sides[0] + sides[1] > sides[2] print(is_valid_triangle(3, 4, 5))

Output: True

In this code, the list of sides is first sorted to identify the smallest and largest sides without assuming their order. The function `is_valid_triangle()`

compares the sum of the two smaller sides to the largest side, again returning `True`

for a valid triangle.

## Method 3: Using a More Pythonic Approach

We can employ tuple unpacking and the all function to check the validity of the triangle more succinctly. This is more in line with typical Python coding practices and readability.

Here’s an example:

def is_valid_triangle(*sides): a, b, c = sorted(sides) return all([a + b > c, a + c > b, b + c > a]) print(is_valid_triangle(3, 4, 5))

Output: True

In this method, `is_valid_triangle()`

uses asterisk (*) to take any number of arguments and sorts them. The sorted sides are then unpacked into variables `a`

, `b`

, and `c`

. The built-in function `all()`

checks all conditions at once, which improves readability and maintains the function’s purpose.

## Method 4: Using Object-Oriented Programming (OOP)

The OOP method encapsulates the triangle validation logic within a class, enabling more sophisticated data manipulation and the potential for extending the functionality.

Here’s an example:

class Triangle: def __init__(self, a, b, c): self.sides = sorted([a, b, c]) def is_valid(self): a, b, c = self.sides return a + b > c triangle = Triangle(3, 4, 5) print(triangle.is_valid())

Output: True

The `Triangle`

class is created with an initializer that sorts the sides. The method `is_valid()`

checks the triangle validity within the context of an object. This structure allows for more complex geometric calculations and storing additional attributes of the triangle if needed.

## Bonus One-Liner Method 5: Using a Lambda Function

The lambda function provides a concise one-liner approach to check the validity of a triangle, largely used for simplicity in cases where a full function definition isn’t necessary.

Here’s an example:

is_valid_triangle = lambda a, b, c: a + b > c and a + c > b and b + c > a print(is_valid_triangle(3, 4, 5))

Output: True

This one-liner uses a lambda function that takes three arguments and immediately applies the validation conditions. It’s a compact version of Method 1 and is best used in simple scripts or within a larger function for clarity.

## Summary/Discussion

**Method 1:**Basic Conditional Statements. Strengths: Easy to understand and implement. Weaknesses: Can become verbose with more complex conditions.**Method 2:**Sort and Compare Technique. Strengths: Ensures proper comparison by sorting. Weaknesses: Slightly less efficient due to sorting.**Method 3:**Pythonic Approach. Strengths: Improved readability and conciseness with Python-specific features. Weaknesses: May not be as immediately clear to newcomers to Python.**Method 4:**Object-Oriented Programming. Strengths: Easily extendable and maintainable with encapsulation. Weaknesses: Overhead of class structure for a simple task.**Bonus Method 5:**Lambda Function. Strengths: Extremely concise, good for inline use. Weaknesses: Can reduce readability in complex situations.