Folding is more powerful than ruler and compass constructions. One can do cube roots, angle trisections and more.

Coincidentally enough, I had mentioned straight edge and ruler constructions in a different thread a few minutes ago

https://news.ycombinator.com/item?id=47112418

Related older thread

https://news.ycombinator.com/item?id=45222882

That is really cool. I wish it had an animated video to display the result, that'd be even easier to follow and therefore even more impressive.

Maybe possible with that DSL the YouTube channel 3Blue1Brown created?

Manim

I enjoy when HN surfaces out-of-the-box type stuff like this. Very cool.

“outside of the box”?

Is this brute forcing, or is there more to it?

There's more to it. Origami as a calculation tool is more powerful than compass and straight edge.

Is there? I followed the link[1] to the original author of the desktop software this web app is derived from, and he says:

> To make a long story short, by the third generation of ReferenceFinder (written in 2003), I had incorporated all 7 of the Huzita-Justin Axioms of folding into the program, allowing it to potentially explore all possible folding sequences consisting of sequential alignments that each form a single crease in a square of paper. Of course, the family tree of such sequences grows explosively (or to be precise, exponentially); but the concomitant growth in the availability of computing horsepower has made it possible to explore a reasonable subset of that exponential family tree, and in effect, by pure brute force, find a close approximation to any arbitrary point or line within a unit square using a very small number of folds.

(emphasis added)

[1] https://langorigami.com/article/referencefinder/

There's brute force involved, but it's not brute force by itself. It's like a chess engine, which yes, it checks thousands of positions, but only after filtering out hundreds of thousands of positions.

Are you involved in writing or maintaining this software? If so can you provide some more details on this “filtering”? Because I skimmed the source code [1] and it looks to me like it’s pure brute force building a database of lines and points up to a certain rank (number of operations required to create that line/point) and then searching through it.

[1] https://github.com/MuTsunTsai/reference-finder-cpp/blob/main...

No, you are right. The author even uses the expression "by pure brute force". I just supposed it would given that virrually every number a user would input is constructible with foldings.

Folding could be called a superset of measuring.

Measuring could be called a special case of folding (it's an accordian fold)