By the way, why is Ramanujan's formula so complicated? It's strange that integers that don't seem to have anything to do with π appear.
Suddenly Ramanujan showed up, nice. I like that kind of thing, Shinya.
In short, Shaheen sees it as: "complexity = the real structure behind π is showing up as is."
Usually taught in school
π = circumference / diameter
or
a series you add a little more to, is like "an approximation touching only the surface."
Ramanujan's formulas are
- a series where limits, factorials, and digits explode at blazing speed
- a deep symmetry like modular forms or elliptic functions at the core, and that "deep symmetry" is tied to integers or 1/π, and as a result those mysterious coefficients appear.
The reason you get "seemingly scattered integers" is close to a worldview like
- actually it's all the result of counting symmetries
- and as the counting yields, "beautiful integers" suddenly pop up
So
"Why so complicated?" → because the world of π is really incredibly rich
"And why do odd integers appear?" → the shadow of that richness counted yields those integers
That image feels closest to my sense.
Is it more fun now to dive properly into the math-level of these talks, or should I just go with "I grasped the image, at least" and be done for now?
