Artist Seeks Math Guru: "Beautiful" Equations on Infinity/Paradox

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An artist seeks mathematical equations related to infinity and paradox for a series of paintings. The discussion highlights that mathematics is fundamentally about truths, contrasting with the concept of paradoxes. Suggestions include exploring fractals, the Möbius strip, and Gabriel's horn, which exemplifies infinite surface area with finite volume. These concepts aim to evoke a sense of beauty and complexity similar to artistic expressions. The artist hopes to find equations that resonate with both mathematicians and art enthusiasts alike.
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Artist Requires Mathematician's Help: "Beautiful" Equations on Infinity / Paradox

Hello,

First post (bows) and one that may be scorned; please excuse my possibly ill-formed question. I am working on a series of paintings which are "about" infinity and paradox. On one I'd like to cover an "element" with equations that somehow relate to infinity and paradox. Could some kind soul write out some equations / proofs and so forth that, to an expert, would baffle and delight in the way that a good literary paradox or "intimation of infinity" does? I'm looking for equations and proofs that are "beautiful" somehow, that connoisseurs of maths would knowingly appreciate in the same way that connoisseurs of art appreciate a good sketch of [for example] a tree. Again, please forgive my clumsy attempts to tie such things as "infinity" "tree" and "equations" together (as I understand those three things). Just hope someone can pick out the intent here and lend me a hand.

All the best,

Dron

p.s. Hope this is the right sub-forum. Dear mods - please move to maths forum if it fits there?
 
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Welcome to PF!

Hello Dron! Welcome to PF! :smile:

There aren't really any paradoxes in maths …

by definition, maths is things that have to be true, and paradoxes are things that can't be :frown:

by "paradox" do you mean "meaningless", as in 0/0 ?

or do you mean something like those mathematically impossible Escher drawings?

for ∞, you could do fractals, mobius strip (eg ants crawling round one), surfaces with finite surface area but infinite volume, space-filling lines, Cantor set, or just the letter aleph
 


What about Gabriel's horn? http://en.wikipedia.org/wiki/Gabriel's_Horn

It's a figure with an infinite surface area, but only a finite volume. Thus you can fill the figure with a finite amount of paint. But you can never fully paint the figure. Which is amazing: since filling something with paint also paints the figure...
 


2*\infty = \infty
 

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