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Lakes of Wada

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Re: Lakes of Wada

#11

Post by cousin_it »

semi-extrinsic wrote: post #6

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 fr…

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.

Re: Lakes of Wada

#12

Post by thecopy »

oliveshell wrote: post #3
Roritharr wrote: post #2

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

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 linke…

During my master thesis, i went into the Wikipedia pages for mathematical theorems i mastered and i felt i was five years old.

The language used on the mathematics pages on Wikipedia almost makes me believe it is some sort of intentional gate-keeping scheme.

Re: Lakes of Wada

#14

Post by bbeonx »

Roritharr wrote: post #2

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

Out of curiosity, what wasn't clear aside from openness?

BTW, for those interested, openness is the property assigned to a set of points not containing its boundary. For instance, an open interval (a,b) doesn't contain boundary points a or b. An open unit square is a 1x1 square without it's edges included

Re: Lakes of Wada

#15

Post by Roritharr »

bbeonx wrote: post #14
Roritharr wrote: post #2

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

Out of curiosity, what wasn't clear aside from openness? BTW, for those interested, openness is the property assigned to a set of points not containing its boundary. For instance, an open interval (a,b) doesn't contain boundary points a or b. An open unit square is a 1x1 square without it's edges included

>In mathematics, the lakes of Wada (和田の湖 Wada no mizuumi) are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all have the same boundary. In other words, for any point selected on the boundary of one of the lakes, the other two lakes' boundaries also contain that point.

"disjoint connected open sets" - What is an open set? What does disjoint connected mean?

"plane or open unit square" - I know what a plane is, but the context of an "open unit square" which doesn't make sense to me shakes my confidence in that.

"on the boundary of one of the lakes" - What did we just define as a lake?

Re: Lakes of Wada

#16

Post by nerdponx »

semi-extrinsic wrote: post #6

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 fr…

The construction shown on the page makes me think of this as if the three fluids are infinitely mixed, if that makes any sense.
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