3 ms·

I was trying to search in the paper for a definition of the shape, to, for example, draw it in SVG. It seems there is no closed-form solution. I saw this paper

by ks2048 2y ago

I was trying to search in the paper for a definition of the shape, to, for example, draw it in SVG. It seems there is no closed-form solution. I saw this paper is maybe easier to follow for the definition: https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa.pdf https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa... Quote: It is worth noting that Gerver’s description of his shape is not fully explicit, in the sense that the analytic formulas for the curved pieces of the shape are given in terms of four numerical constants A, B, φ and θ (where 0 < φ < θ < π/4 are angles with a certain geometric meaning), which are defined only implicitly as solutions of the nonlinear system of four equations

robinhouston 2y ago
The downloadable extras at the bottom of https://www.math.ucdavis.edu/~romik/movingsofa/ https://www.math.ucdavis.edu/~romik/movingsofa/ may be useful – especially the Mathematica package, if you have Mathematica.
LegionMammal978 2y ago
Speaking of SVGs, you reminded me of the beautiful SVG documents in David Ellsworth's "Squares in Squares" page [0]. If you view the source of any of them, you'll find the full Mathematica code to generate any constants needed (which is usually simple enough to implement in other CAS software, if you know how to read it), as well as their values listed to dozens of digits within an inline DTD, to be referenced from the actual elements. [0] https://kingbird.myphotos.cc/packing/squares_in_squares.html https://kingbird.myphotos.cc/packing/squares_in_squares.html