All circles would be slightly smaller. - source, am a Professor of Sizemology

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 ………

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

I prefer π = 3.14 ± 0.14. Add a little chaos.

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.

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

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’?”

Probably a lot like Indiana.

Circles would be smaller

Probably a triangle.

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.

Probably the Distortion World.