[dpark]

Hard pass. The exact area of a circle is pi*r^2. We can calculate decimals of pi arbitrarily far, certainly further than our ability to measure. “Exact area” means we use symbolic math, not that we quibble about significant digits.

[Noaidi]

Pi is an infinite number. Each time we calculate the area of a circle with another decimal of pi we get a new answer.

You seem to be avoiding the question of how we can know the exact area of a circle knowing that pi is infinite.

I am saying that the area of a circle is impossible to know. And that has both philosophical and physical ramifications.

Very fact that this well-known scientific truth is hard to accept those people is telling.

https://www.scienceabc.com/pure-sciences/can-the-area-of-a-c...

“Hence, not only is it impossible to ever determine the exact value of the area of a circle, but it is equally impossible to measure any area with 100% accuracy.”

[dpark]

> Pi is an infinite number.

Your own link confirms this is not true. Irrational is not the same thing as infinite.

> You seem to be avoiding the question of how we can know the exact area of a circle knowing that pi is infinite.

I’m not avoiding it. I’m saying it’s a meaningless question. 16 digits of pi will be more precise than essentially anything we can measure. Just 3 digits of pi will probably be more precise than you can measure at home.

If you need perfection, you stick with symbolic math. If you need to convert to absolute physical units, your ability to measure will be your limit, not the irrationality of pi.

> Very fact that this well-known scientific truth is hard to accept those people is telling.

It’s not hard to accept. It’s not interesting. There are no physical problems related to this fact. And no interesting philosophical problems.

Your problem isn’t that you lack the knowledge but that you are overconfident in your ignorance. You lack the curiosity to ask why no one is impressed or convinced by your beliefs, instead assuming everyone else is missing the deep insights you believe you possess.

This is why you can cite someone’s article about everything being quantum waves as support for your personal beliefs while also confidently stating that the article’s author is completely wrong for believing in quantum waves. Because you are not looking for information. You are looking for confirmation. You are rendered blind by your hubris.

[Noaidi]

> Your own link confirms this is not true. Irrational is not the same thing as infinite.

Huh? From the article:

"Pi is a non-terminating and non-recurring irrational number. When we say that pi is infinite, we intend to say that pi has an infinite expression, not an infinite value."

That is what I meat by infinte, as in the number never ends.

I am not commenting about being more precise. I am talking about exactness. Yes, with every didgit we add to pi we become more precise, and there is a limit to what we need, but to know that there is not exact value we can give to the area of a thing, how can we say that is a thing at a deeper level? If we know things because we "measure them" and measuring is never exact, what do we really know?

[dpark]

> to know that there is not exact value we can give to the area of a thing

Pi has an exact value. It is irrational, not inexact.

This is increasingly irrelevant and inaccurate rambling I’m engaging with. I’m out. Take care.