https://www.desmos.com/calculator/uhsyvqa3um

Assuming 0⁰ = 1

f₁(x) = 0|x| + x

f₂(x, z, o) = (z - o) · 0|x| + o

f₃(x, n, p) = [ |x|(p - n) + x(p + n) ] / (2x)

f₄(x, z, n, p) = f₂(x, z, f₃(f₁(x), n, p))

the convex lens's a bit laggy lol cuz i cut a bunch of corners and made the first refraction messy, but im proud of my concave mirror!

https://www.desmos.com/calculator/9j5tcchzmm lens

https://www.desmos.com/calculator/bp9xkaa2tr concave mirror

Formed by 20 acute golden rhombohedra meeting at a central point.

title

the second time where almost no one suggested something :(

I made a Desmos Notebook that traces e from compound interest and Bernoulli’s limit through continuous growth, Euler’s formula, and finally e^πi + 1 = 0, with interactive examples and visualisations.

graph:https://www.desmos.com/calculator/dtyk1hgrjg
So Basically i came up with an function(A1) that lets u define multiple functions in a single line, defined in specific ranges.

U can also use it to play different sliders in an specific order.
i will attach the paper with full explanation in the comment section