My thinking through common equations as if pi was equal to one -- and subsequently thinking about the cultures that might use that -- was brought up in another thread, and is being brought here in order to stop derailing the aforementioned thread.

So... I think I explained it (either that or I did an awful job of explaining it and/or I've been accidentally using wrong terms). By making pi the basis for a common math problem: 2pi * r becomes 2r/pi. In order to make this make sense for a culture, I've surmised that 1/pi would be an irrational number (an "anti-pi") the people use on a common basis in their math.

On the other hand, I could be doing the math wrong.

Yes!

* will reply later *

Oy. Melt my brain and stir it into mush, why don't you? XD Seriously, I'm going to be waiting for the better explanation

Andrew

(As I was starting to try to explain in the other thread ...)

The problem I see is that our whole system is built starting from two foundations: rational numbers (which themselves are founded on counting) and geometry. If a culture considered pi a "rational" number and what we consider rational numbers to be "irrational" ... doing anything with pi inevitably introduces what we call "rational numbers." Jut having it introduces an (implicit) one; adding it introduces a rational number (the count of how many times you're adding it), multiplying it by itself similarly, and so on. (There's a reason many people throughout history have been of the opinion that mathematics is discovered rather than invented.)

*Reads over a few times before the paragraph clicks* I hadn't thought of that. I wonder if there is another way I could give pi extreme importance...

* was confused *

* still is, for that matter *



What I thought you meant before was that your culture's system for interpreting and manipulating mathematics was what you were saying was different. Which system is easily changed. * smiles * What if you made it so that their numeric symbols take their places on the number-line at intervals of Pi?

Here's an idea; I'm not sure how this would work, but I'm fairly sure it could. In one of the accounts I heard or read of "the birth of mathematics" in the Euclidean school, squares (and area as sums of "unit squares") were seen as fundamental because they were working on a floor paved with square tiles. In another world, with utterly different mindsets, unit circles might become the fundamental building block of the most basic geometry, so that the thing you think first to do if you have a lenth is not to draw a square with sides of that length, but to draw a circle twice that length across.
Oh, and another thought from those very early readings (so long ago ...) occurs to me: I'd suggest looking into early Egyptian and Babylonian mathematics, which were very different, and I think were supplanted by the Greek model primarily because (aside from Alexander's conquests and such, which we might call "an accident of history") the Greek model was better at making new mathematical discoveries using its existing ideas as tools, while other cultures' understandings were aimed at solving particular problems.

*melts* I. Don't. Understand. This. AT ALL!!! *makes mental note to steer clear of this thread in order to keep from having a mental break-down*

* giggles * * erases mental note * Did it work?

Ack! My note!

Ah.

That is exactly the kind of thing I was aiming for.
*nods* The numeric system of the Babylonians (or was it Assyrians? *can't remember*) crossed my mind briefly when I was thinking of this. I believe their counting was based on the number sixty instead of ten.
Without thinking through it at all, that sounds like it would work well for my purposes also (perhaps the race divides circles into six wedges as a kind of sub-shape -- our 45-45-90 triangle is to our square as these wedges would be to their circle).

Awww. Math can be so much fun...

You're thinking of the Babylonians; I don't think they counted in base sixty, but that and twelve were their preferred bases for calculating ratios (fractions) of things, as that makes calculations involving simple fractions easier---which is, if I'm not mistaken, why our society divides days into twenty-four hours, hours into sixty minutes, and so on.
The Egyptians, I think I remember, had a way of calculating the area of a field (or maybe how much water it would need, or something) that a modern mathematiian could only have drived using integral calculus, and similarly "advanced" techniques related to their building projects---but, as I said, they didn't generalize these or apply them to less-pressing problems.

Sort of like in the proof (if I remember correctly) of the correctness of the formula for the volume of a sphere?


As the protagonist of Robert A. Heinlein's Have Space Suit---Will Travel put it, "Math is worse than peanuts."

Ah. Fractioning is what I was thinking of anyways.
Interesting.

I don't think I'm familiar with that proof... (Come to think of it, I'm not familiar with any proofs. Geometry was three-to-four years ago. )

I ran across that one in second-semester calculus in college, if I remember correctly, and actually in one of the later chapters in the book rather than anything we actually overed in class. And I only vaguely remember it, I'm sorry to say.

Not only is this not right, it isn't even wrong! (Unless I've completely misunderstood what you meant).

The value of π is what philosophers call a necessary truth. One can't imagine a world, much less can there be a race, for which the value of π is not 3.14159...

Now, you could, conceivably, have a base-π counting system, but I don't think it would by any stretch approach the criteria to be considered useful. And even if you did, π would not equal 1. In a base-ten counting system, you have places for 1, 10, 100, etc. In a base-two system, you have places for 1, 2, 4, 8, 16, etc. In a base-π system, you would have places for 1, π, π^2, π^3, etc. See the pattern? In any counting system, the first place is 1.

In short, to ask "what if π were equal to 1?" is meaningless. It is like asking "what if 2 were equal to 1?"

That's too bad, kingjon.

Thanks for posting Samstarrett

On a side note, I've considered something similar to that recently. (I really need to find the time to make that thread...)

Ya'll are amazing. Just saying.

*staggers out of thread feeling slightly dizzy*