I’ve been delving into some fascinating patterns in mathematics lately, and I stumbled upon something really intriguing: the triangle of numbers where each number is the sum of the two numbers directly above it. It comes from what many people know as Pascal’s Triangle, and it’s not only interesting but also has a ton of applications, especially in combinatorics and probability.
Here’s how it works. You start with a single ‘1’ at the top of the triangle. As you work your way down, each number in the triangle is formed by adding the two numbers directly above it. So, for example, the second row would be ‘1 1’, since each side of the top ‘1’ has no number beside it, which is treated as 0. The next row would then be ‘1 2 1’ since 1+1=2.
Now, I’m curious if you could whip up a function that generates this triangle for a given number of rows, say ‘n’. Think about it—if ‘n’ equals 4, you would have:
“`
1 (Level 0)
1 1 (Level 1)
1 2 1 (Level 2)
1 3 3 1 (Level 3)
“`
What I picture is a list of lists, with each inner list capturing the numbers at each specific level. So, at level 0, you’d have `[1]`, at level 1, `[1, 1]`, and so on.
Now, here’s the challenge: Can you create a function that takes this integer input ‘n’ and then outputs this beautifully constructed triangle? I imagine you’d probably want to loop or utilize some kind of recursive function to get it just right.
What do you think? I’d love to hear how you would approach this problem! Also, once you have it down, maybe even try to visualize the output in a way that makes it easy to see how the numbers build from one level to the next. Let’s see if we can tackle this puzzle together!