You might find this interesting: Non-Euclidean Doom: what happens to a game when pi is not 3.14159…
The magic starts at 6:47
this post was submitted on 23 Jan 2025
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It starts to get really funky.
The video and the effects of different pi values are sick! But I've never heard such a bad speaker. Speaking in front of an audience isn't the strong suit of this guy
This comment is kinda mean. He successfully engaged the audience and even makes them laugh while informing them on his topic. I'm curious to hear what qualifies him as a "bad speaker" in your mind.
This doesn't directly answer your question, but things would probably get very weird compared to our universe. Here's an interactive visualization of a different weird universe with two time dimensions, Dichronauts by Greg Egan:
https://www.gregegan.net/DICHRONAUTS/02/Interactive.html
He really goes through the math on that site, so you might get some insight into how other topologies would look
Whoa. That's over my head.
I prefer π = 3.14 ± 0.14. Add a little chaos.
Probably a lot like Indiana.
OOF!
I suppose you could redefine pi to be exactly like 3, but you'd have to change the value of 1 to be equal to (π/3) which would make it very difficult to buy bananas.
I don't buy bananas, so this isn't relevant to me.
if pi was 3, the area of a circle would be equal to 3 squares with side-length of the radius. this means the definition of a circle would be different, since now a circle is 3 squares. This would break geometry. Since the definition of a circle is the foundation of geometry, and trigonometric functions sin and cos.
Hmm
or maybe if the area of a circle A=r*r*PI and PI = 3 so A=r*r*3 you would just scale the radius by the factor of sqrt(pi)/sqrt(3) = 1.0233267079464885... to get to a correct circle again.
So you would just scale the universe by a factor slightly larger than 1, up-scaling everything.
But then the formula for the volume of a sphere V=4/3*pi*r*r*r would break ………
This question does not make sense. π is an abstract mathematical constant whose value has absolutely nothing to do with the physical world. It’s like asking “what would the universe look like if the word ‘fish’ started with ‘p’?”
"what would the universe look like if the word ‘fish’ started with ‘p’?”
More tie dye, for one.
Oh, no way!
Pi as in math like Euler’s identity, cannot be changed. It arises from the definition of e and imaginary numbers, both of which arise from the natural numbers which arise directly from axioms.
Pi as in the ratio of a circle’s circumference to its diameter, however, could be changed, in which case you would change the fundamental geometry of space. This would be neither hyperbolic nor spherical space because those spaces still use the mathematical pi for determining angles (along with hyperbolic trig functions of course).
The geometry would likely be much closer to Chebyshev or Taxicab space since the ratio of circumference to diameter in those spaces is 4 (I think…). Because of this, I suspect that using a distance function like in Chebyshev or Manhattan but with a triangular grid instead of a square one would yield this exact situation where geometric pi=3. This would be confusing as hell but now I’m curious and have coincidentally already started exploring the concept of metric spaces so I’ll look into it. Though I’ll probably get distracted and forget…
Edit: Found it, Chebyshev distance on hexagonal grid would give a circumference/diameter ratio of 3. So a metric space with a distance function like that is the geometry you want.
Circles would be smaller
Wait...
All circles would be slightly smaller. - source, am a Professor of Sizemology
Probably a triangle.
Like a curved triangle that's actually a circle?
You universe's pi doesn't equal pi... it equals 3...
But can it run Doom?
https://youtube.com/watch?v=_ZSFRWJCUY4&t=450s
Yes. Mostly.
Spatial cohesion worsens as pi diverges from... pi.
What game is that? The background noise was just a dude saying distortion over and over again
Pokémon Platinum. Towards the end of the game, you meet the villain in the game's version of Hell, known as the Distortion World. The background noise was likely put in there as a joke.