Title: Understanding Pascal’s Triangle and writting code CODE

Pascal triangle illustration

Pascal’s triangle is a fascinating mathematical(ooh scary )concept named after the French mathematician Blaise Pascal. it is like a simple pyramid of numbers. Imagine starting with the number one at the top. Then, as you go down each level, every new number you see is just the sum of the two numbers directly above it to the left and right. If there’s only one number or no number directly above, you just use the number that’s there (or if there’s none, you pretend there’s a zero). This way, each level has one more number than the level above it, forming a neat triangle. It is a triangular array of binomial (The binomial coefficient represents the number of ways to choose ( k ) elements from a set of ( n ) elements without considering the order of selection)coefficients, where each number in the triangle represents the sum of the two numbers directly above it in the previous row.

A NONE Math loving Girl approach to constructing a Pascal triangle:

1. Define Function: Start by Constructing/defining a function that generates Pascal’s triangle up to the nth row. This function will serve as the foundation for your code.

2. Parameters and Return: Understand the parameters the function will take, such as the number of rows for Pascal’s triangle, and what it will return, which is a list of lists representing the triangle.

3. Pascal Triangle: Acknowledge the fundamental concept of Pascal’s triangle as a triangular array of binomial coefficients. This understanding is crucial for implementing the logic to generate the triangle.

4. Logic(short pseudocode while drawing on piece of paper what l really want to create given the defination of pascal triangle : Follow a systematic approach to construct the Pascal triangle:

- Outer Loop (Rows): Iterate over each row of the triangle. Use a loop that goes from 0 to the desired number of rows.

- Inner Loop (Columns): Within each row, iterate over each column. The number of columns in each row is equal to the row number plus one.

- Calculating Values: Calculate the value for each cell in the triangle. Each cell’s value is the sum of the value directly above it and the value diagonally above and to the left of it.

- Printing Values: Print the values of each cell in the triangle, or store them in a list for later use.
- Repeat: Repeat the process for each row, updating the values accordingly.

5. Conditionals: Incorporate conditionals to handle specific requirements or constraints. This could involve checking for valid inputs or adjusting the triangle’s appearance based on certain conditions

By following this structured approach, you can effectively implement Pascal's triangle generation in Python or any other programming language. This understanding not only helps in coding but also enhances mathematical comprehension and problem-solving skills.

#!/usr/bin/env python3

"""
This script defines a function to generate Pascal's triangle up to the nth row.
"""

def pascal_triangle(n):
    """
    Generate Pascal's triangle up to the nth row.

    Args:
        n (int): Number of rows for Pascal's triangle.

    Returns:
        list of lists: Pascal's triangle up to the nth row.

    Raises:
        ValueError: If n is less than or equal to 0.
    """
    if n <= 0:
        return []

    triangle = [[1]]

    for i in range(1, n):
        row = [1]
        for j in range(1, i):
            row.append(triangle[i-1][j-1] + triangle[i-1][j])
        row.append(1)
        triangle.append(row)

    return triangle