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.
Was going to say the same. Also π isn't infinite. Far from it. it's not even bigger than 4. It's representation in the decimal system is just so that it can't be written there with a finite number of decimal places. But you could just write "π". It's short, concise and exact.
And by that definition 0.1 is also infinite... My computer can't write that with a finite amount of digits in base 2, which it uses internally.
So... I'm crying salty tears, too.
[Edit: And we don't even need transcendental numbers or other number systems. A third also doesn't have a representation. So again following the logic... you can divide a cake into 5 pieces, but never into 3?!]
I thought that was the joke in the comic? That we can't know numbers exactly that have an infinite decimal expansion. That'd be true for some rational numbers like a third, if you change the basis of the numeral system it'd be different numbers. And irrational numbers too if you have a integer base. But I'd argue how we write down a number isn't what determines exactness or 'infinity' by the words of the comic.
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.
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.
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.
In the spirit of the meme this does not constitute "finding" the radius.
There doesn't exist a radius for which both the radius and the circumference are rational numbers.
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.
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More likely a mathematician would correct you instead of crying. Pi is not infinite, its decimal expansion is infinite!
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.
Mathematicians taking a physics class and being told they have to round things. That’s when the tears start flowing.
Its decimal expansion is finite in the base pi.
1?
No 10. 1 is the same number in any base.
In my experience, 1 is equivalent with 1’s in other base.. this particularly applies for base-ball
This is the correct answer. Pi is known. What it's decimal expansion looks like is irrelevant. It's 1 in base Pi.
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
Try it when you find some physicist that cares about exact values. Or when you see pigs flying over your head, both are about as likely.
Perfectly spherical pigs?
Would go well with my former teacher's point-shaped cows.
I see, you were never at a Pink Floyd concert
Exactly, a fraction is completely as valid of a way to express a number as using a decimal.
1/2 = 0.5
They're both fully valid ways to write the exact same quantity
This was my first thought and then I realized I had been nerd sniped.
Easy. Take a wire that is exactly 1 meter long. Form a circle from the wire. The circumference of that circle is 1 meter.
uh huh. and how are you measuring that?
Now the engineers and/or scientists are crying
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.
He obviously meant to say how do you measure that it’s exactly 1m, even when still in a straight line. Exactly being the key word here.
But is the circumference of the outer circle or inner circle 1m? The wire has a nonzero width.
I don't have to measure it. I stick under glass and define it as the standard which all other measurements are derived from.
I will be measuring it in meters. One. There you go.
Ok, you got another source of water - physicists.
Plancks
Exactly. Use a laser measure to cut a plank, then use that for reference!
Laser Measure.
Not true. If you define the circumference in terms of pi, you can define the circumference exactly.
"Find" not "define"
Putting things in base 10 is also a definition. Digits aren't special.
Was going to say the same. Also π isn't infinite. Far from it. it's not even bigger than 4. It's representation in the decimal system is just so that it can't be written there with a finite number of decimal places. But you could just write "π". It's short, concise and exact.
And by that definition 0.1 is also infinite... My computer can't write that with a finite amount of digits in base 2, which it uses internally.
So... I'm crying salty tears, too.
[Edit: And we don't even need transcendental numbers or other number systems. A third also doesn't have a representation. So again following the logic... you can divide a cake into 5 pieces, but never into 3?!]
Can pi be expressed with a finite amount of digits in another number system?
How about a pi based system, then pi is 1.
You're correct.
For reference: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration
Possible, but then the diameter would be an irrational number
I don't think there's any technical reason we can't count in base pi
I'm pretty happy with being able to write integers in a finite number of digits. Wouldn't want to give that up.
Well we need an integer base number system....
"A base is usually a whole number bigger than 1, although non-integer bases are also mathematically possible."
https://simple.m.wikipedia.org/wiki/Base_(mathematics)
Not sure where you're going with the decimal thing. Pi had infinite digits in any integer base because it's irrational.
I thought that was the joke in the comic? That we can't know numbers exactly that have an infinite decimal expansion. That'd be true for some rational numbers like a third, if you change the basis of the numeral system it'd be different numbers. And irrational numbers too if you have a integer base. But I'd argue how we write down a number isn't what determines exactness or 'infinity' by the words of the comic.
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)
Also
Pi = 4! = 4×3×2 = 24
Omfg why can’t I figure out why this does not work. Help me pls
I think it's because no matter how many corners you cut it's still an approximation of the
circumferencearea. There's just an infinite amount of corners that sticks outYes. And that means that it is not an approximation of the circumference.
But it approximates the area of the circle.
True, thanks for the correction
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.
But if you made a regular polygon, with the number of sides approaching infinity, it would work.
https://youtu.be/VYQVlVoWoPY
Exactly what I was expecting haha(I mean the video)
The lines in this are askew and it's mildly annoying
They're there to askew why the logic doesn't work.
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.
Who said Pi is infinite? If we take Pi as base unit, it is exactly 1. No fraction, perfectly round.
Now everything else requires an infinite precision.
Eek, that makes my skin crawl. Taking what you said literally would imply that π² = π.
pi equals 10
Engineers be like:
I'm pretty sure a base-Pi counting system would mean that Pi is π, not 1.
You'd count π, 2π, 3π, 4π, and so on. It doesn't change reality, just the way you count and represent numbers.
I might be off, but it's definitely not π = 1.
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..
I'm confused, how is pi used as a unit? My understanding is that it's a number
6π is an acceptable answer for finding the circumference of a circle with a radius of 3 units of something.
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.
Let's say you got a circle with radius 1/π...
came here for this
Yeah, calling pi infinite makes me wanna cry, too.
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.
Not if your diameter is d/pi. Then your circumference is d, where d > 0.
Check mate atheists.
Ftfy.
Well now you can't find the radius
Radius = d/(2*pi)
In the spirit of the meme this does not constitute "finding" the radius. There doesn't exist a radius for which both the radius and the circumference are rational numbers.
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.
Achilles and the Tortoise paradox.
Joke's on them, tears are too salty to provide hydration.
The circumference of a circle with a diameter of 1 cm is exactly π cm. There you have it.
m e a s u r e
Bah, the universe is too messy and disordered to be worth the trouble
Besides measuring it with a measuring tape.
Pi is 3.
Ah, the Euler identity. 3^i ^3 -1=0
Rofl :D Well, close enough, and about as sexy when a bit drunk.
Ahem. MathEmaticians.
Prove it.
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.