ReferenceFinder: Find coordinates on a piece of paper with only folds
mutsuntsai.github.io78 points by icwtyjj 5 days ago
78 points by icwtyjj 5 days ago
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
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.
I enjoy when HN surfaces out-of-the-box type stuff like this. Very cool.
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)
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.
Folding could be called a superset of measuring.
Measuring could be called a special case of folding (it's an accordian fold)