Re:ReferenceFinder: Find coordinates on a piece of paper wit...
by CrazyStat on Sunday February 22, 2026 @03:45PM
(#47114484)
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.
Re:ReferenceFinder: Find coordinates on a piece of paper wit...
by PowerElectronix on Monday February 23, 2026 @11:38AM
(#47124703)
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.
Re:ReferenceFinder: Find coordinates on a piece of paper wit...
by CrazyStat on Monday February 23, 2026 @02:06PM
(#47127122)
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.
Re:ReferenceFinder: Find coordinates on a piece of paper wit...
by PowerElectronix on Monday February 23, 2026 @06:35PM
(#47130644)
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.
> 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/
[1] https://github.com/MuTsunTsai/reference-finder-cpp/blob/main...
Folding is more powerful than ruler and compass constructions. One can do cube roots, angle trisections etc.
It's a strange coincidence that I commented about straight edge and ruler constructions in a different thread.
https://news.ycombinator.com/item?id=47112418
Related thread from several months ago
https://news.ycombinator.com/item?id=45222882
Measuring could be called a special case of folding (it's an accordian fold)