The Quest to Find Rectangles in a Square | Hacker News Reader

The Quest to Find Rectangles in a Square

nytimes.com

118 pointsgumby27 comments

Ian Henderson's own post on the process is probably more interesting for most people here.

http://ianhenderson.org/similar-rectangles/

Hey, that's me! Though I mention it in the post, I also want to give a shoutout here to libcalcium, which handles the somewhat magical task of representing and comparing exact algebraic numbers: https://fredrikj.net/calcium/index.html.

Loving it. Pretty good in an art sense too, playing with proportions in both a mathematical as well a visual way. Makes me want to brush up my mathematics

This is super interesting. I am particularly curious whether the resultant series correlates with any other know series arising in other areas...

Wow! I had no idea you could get fun projects like this into the NYT.

How did you do it? :-D

The author[0] writes a monthly column on puzzles and other recreational math. She was the author of John Horton Conway's biography[1] and many other math-related and math-adjacent things.

People writing monthly columns are always under pressure to find things that are new and can be made accessible, so if you have something that fits the subject and brief, it's easy. The problem is that most things you think are fascinating, the authors/journalists won't think is interesting, so you may need to sell them on it.

[0] Siobhan Roberts

[1] Roberts, Siobhan (2015). "Genius at play: The curious mind of John Horton Conway." Bloomsbury. ISBN 978-1620405932.

Also John Baez's posts

https://golem.ph.utexas.edu/category/2022/12/dividing_a_squa...

https://golem.ph.utexas.edu/category/2022/12/guillotine_part...

Oh. Gosh. I've been mentioned by name in the NY Times.

Congrats Colin!! Next thing you know, late night TV will be calling :)

The New York Times' effect on [a] man.

The original discussion first posted here:

https://mathstodon.xyz/@johncarlosbaez/109511663915548794

https://archive.ph/qouZA

Can we just skip to the part where 500 years from now this is essential for ftl travel?

Is this an OEIS sequence yet?

It is, as of today! https://oeis.org/A359146

Is this the first non-meta[1] mention of Mastodon in the NYT?

[1] By this I mean a mention that isn't in the context of Mastodon as "a decentralized alternative to Twitter" or similar. Instead I'm referring to something that actually happened on Mastodon.

I tried and came up with three of the eleven, ha ha. One of mine isn't among the eleven though. I'm too thick though to figure out if I made a mistake with it. I tried computing the ratio with algebra but I'm a little rusty.

The one I came up with for 6 rectangles (divide the square down the middle on one axis, then into thirds on the other axis) I didn’t see in the 245 at the bottom of the article. I might have just skipped over it, but that one seems pretty trivial to me, so if they missed it, there must be some issue with their method.

Edit: I think I misunderstood. They are interested in the number of unique ratios, not including different ways that rectangles of the same ratio could be drawn to fill a square. The pictures just show one example of how the rectangles of each ratio could fill a square.

For my example, it looks like they have a square that is divided into the top third and bottom two-thirds, then the top third is divided in half, then the left half of that is divided into quarters. That’s another way of fitting six rectangles of ratio 1:1.5 into a square, besides the way I described above.

Yeah, exactly -- if you're curious, here are the 1:1.5 ratio 6-rectangle dissections after disabling all the code that removes duplicates: https://i.imgur.com/jbZcpFT.png

Only the proportions of the rectangles matter, not their position.

This is what dealing with #@$!&% CSS feels like. Give me back WYSIWYG grids with optional "stretch zones", they can do 90% the same thing with 2% the headaches.

You got it fam. https://css-tricks.com/snippets/css/complete-guide-grid/

Its integration with other HTML widgets is shaky.

HTML doesn't have "widgets" though, so whatever you're thinking of, that's not HTML and CSS, that's "some framework that decided to run its own course".

All these squares make a circle.

All these squares make a circle...

https://en.wikipedia.org/wiki/Squircle

https://en.wikipedia.org/wiki/Squarial

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