Plus even that isn't enough: 10/3 has an infinite decimal expansion (in base 10 at least) too, but if π = 10/3, you'd be able to find exact circumferences. Its irrationality is what makes it relevant to this joke.
A mathematician is also perfectly happy with answers like "4π" as exact.
Plus what's to stop you from having a rational circumference but irrational radius?
Writing this, I feel like I might have accidentally proved your point.
Yup, similar to the square root of two and Euler's number.
These are numbers defined by their properties and not their exact values. In fact, we have imaginary numbers that don't have values and yet are still extremely useful because of their defined properties.
The actual punchline here should have been “there is no known equation to calculate the exact perimeter of an ellipse”, then sucking tears from an astrophysicist
You don't need to, it's defined. (Lol). If you take a circle with a circumference of 1, then its circumference will be 1... I think I might have lost some braincells reading this.
You still think in 1-based system, Pi unit * Pi unit is Pi of Pi units or 3.14159.. Pi units.
Also, Pi unit / Pi unit is 1/Pi Pi units or 0.318309886183790.. Pi units..
1 is also a number, a number we chose by convention to be a base unit for all numbers. You can break down every number down to this unit.
20 is 20 1s. 1.5 is 1 and a half 1.
If we have Pi as a unit, circumference of a circle would be radius*2 of Pi units. But everything that doesn't involve Pi would be a fraction of Pi, e.g. a normal 1 is roughly 1/3 of Pi units, 314 is roughly 100 Pi units, etc. etc.
That doesnt make a difference. You can find the exact circumference of a circle, you just cant express it in the decimal system as a number (thats why we have a symbol for it so you can still express the exact value)
I think it's because no matter how many corners you cut it's still an approximation of the circumference area. There's just an infinite amount of corners that sticks out
It's a fractal problem, even if you repeat the cutting until infinite, there are still a roughness with little triangles which you must add to Pi, there are no difference between image 4 and 5, the triangles are still there, smaller but more. But it's a nice illusion.
Because you never make a circle. You just make a polygon with a perimeter of four and an infinite number of sides as the number of sides approaches infinity.
That approach works for area but not for perimeter, because cutting off the corners gives you a shape whose area is closer to the circle's, but it doesn't change the perimeter at all.
If only mathematicians had a number for that. Ya know, the people famous for making names for things on average once per published paper, most of them completely useless.
Technically you can't measure anything accurately because there's an infinite amount of numbers between 1 and 0. Whose to say it's exactly 1? It could be off by an infinite amount of 0s and 1.
And you can't trust anything calculated with an imaginary number. Common guys, it's right there. It's imaginary like the, totally not AI, person I'm pretending to be.