Are there alternate geometries where pi is a different number? (e.g. Non-euclidean geometries)

Question

If you can make a weird non-euclidean mathematical space where parallels lines actually *do* touch eventually, can you make a weird mathematical space where the ratio between a circle’s circumference and its diameter is something other than 3.14159…..etc.? Is there a geometry I don’t know where “pi” is just 3, for instance?

Following from that, the universe as we know it is based on certain fundamental properties, and I’ve heard speculation that there may be other universes (within a multiverse) that have different fundamental properties. In theory, could there some other universe where pi is 3?

In: Mathematics

Answer 1

Surprisingly, pi is also an important constant in a field unrelated to geometry. For example, in Normal Distribution, the PDF is calculated via [this formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/a45cef4ca1e2fcd4d367ecff5806d8a2878d3821). This instance of pi will be the same regardless of the geometry of our world.