I stumbled upon this really fascinating concept about representing integers in base pi, and I can’t help but wonder how it works in practice. You might already know this, but pi isn’t just a number; it’s an irrational, non-repeating decimal, which means translating an integer into base pi isn’t as straightforward as converting it into base 10 or even base 2.

So, I’ve been thinking about how we can create a challenge around this whole idea! Here’s what I’m imagining: Let’s say we want to represent integers in base pi. For instance, if we take the integer 3, how in the world would that look in base pi? We could get creative and represent it as a sum of some fractions of powers of pi. I read that the digits would be in the range of 0 to 9 (just like in decimal) but we’d actually be using pi as the base for our number system.

Here’s a fun thought: Instead of just focusing on the output representation, what if we also created a function that converts intermediate fractions back to a more comprehensible form afterwards? For anyone who takes a stab at this, how would you tackle rounding? And how could we ensure that the results are the simplest fractional forms?

Oh, and one more thing—how about defining a way to compare two integers in base pi to determine which one is “greater”? I can only imagine the headaches this could create!

Let’s test our creativity and coding skills! If you think you’ve got a way to tackle this, how would you approach the problem? Maybe even share your own implementation! I’d love to explore multiple ways to arrive at solutions. Who knows, we might unearth some cool mathematical insights along the way! I’m super curious to see what you all come up with.