
Lakes of Wada - ramgorur
https://en.wikipedia.org/wiki/Lakes_of_Wada
======
semi-extrinsic
So imagine you have three fluids that don't mix which are colored red, green,
blue. You can make drops of these fluids on a piece of paper, and manipulate
their shapes e.g. with a pipette.

This article is saying that mathematically, it's possible to make three
single, continuous but weirdly shaped drops of these fluids, that together
fill a square, in a way such that if you consider the three drop outlines as
seen from above (e.g. by a camera), they all have the same outline.

~~~
cousin_it
Well, they all have the same boundary points. A boundary point is a limit of a
point sequence lying inside the shape. But if we define a different concept of
"outline point" as a limit of a _path_ lying inside the shape, then I think
the three shapes won't have the same outline.

------
Roritharr
This entry needs a simple english page. I read the first paragraph and didn't
understand anything.

~~~
oliveshell
The article indeed conveys no meaning at all to those not acquainted with the
mathematical jargon it relies on.

Many scientific Wikipedia articles have improved in this regard over the last
few years, but this one (along with many others in the field of mathematics)
remains of little interest to non-mathematicians unready to synthesize and
internalize the vast quantity of information in the articles of relevant
linked terms.

I don’t see this changing any time soon without a lot of concerted effort.

(For the record, I’m someone who did not grok the significance of the
article’s subject in the slightest.)

~~~
bllguo
OTOH the vast vast majority of people who will be reading this will be
mathematicians who are familiar with the jargon. IMO it's perfectly fine for
wikipedia to optimize for the primary audience, instead of optimizing for the
rare curious person who has no relevant background.

~~~
ianai
There’s too much math to fit into one brain. It’s infeasible to expect every
topic explained to a common denominator. Though, I definitely invite anyone
interested to grok through all the math they can and cannot understand. Math,
I hope, is more than just the academic practitioners.

I can attest to the enjoyment value in reading through math way beyond and
outside my understanding. It’s amazingly beautiful, humbling, and can be
surprisingly useful.

------
fibo
It is one counterexample in Topology for the Jordan Curve Theorem.

------
vortico
Wada basins exist for any number of open sets. As you could probably guess
from the article, the Newton method applied to x^n - 1 gives a Wada basin of n
sets. These are fun counterexamples to the claim "given three nontrivial
disjoint sets on a plane, their boundaries are not mutally equal."

