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

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Homework Help Overview

The discussion revolves around the intersection of mathematics and art, specifically focusing on concepts of infinity and paradox. The original poster seeks equations or proofs that embody beauty and complexity, akin to artistic representations of these themes.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the nature of paradoxes in mathematics, questioning the definition and existence of paradoxes within mathematical truths. Suggestions include various mathematical constructs related to infinity, such as fractals and the Cantor set. The concept of Gabriel's horn is introduced as an example of a figure with infinite surface area but finite volume.

Discussion Status

The discussion is ongoing, with participants offering ideas and examples that align with the original poster's request. There is a mix of interpretations regarding the meaning of "paradox" in a mathematical context, and various mathematical concepts are being explored without reaching a consensus.

Contextual Notes

The original poster expresses uncertainty about the appropriateness of the forum for their question and seeks clarification on the relationship between artistic concepts and mathematical expressions.

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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...
 


[tex]2*\infty = \infty[/tex]
 

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