Besides #MathSky #MathArt #Geometry #Origami, neglected to include also: #ArtMath #Mathematics and 🧪

Each annulus alternates mountain folds with valley folds.
It is not yet proved that this folding "exists" in the sense that only the circular creases are necessary. Strong numerical evidence, but not formally proved.
#MathSky #MathArt #Geometry #Origami

Cambridge University Press.
www.cambridge.org/core/books/m...
#MathSky #Mathematics 🧪 #Geometry #Origami #MathArt

In fact in this example, 3 guards suffice. Minimal guarding is an NP-hard problem, i.e., intractable.
#Mathematics #MathSky #GraphTheory
www.science.smith.edu/~jorourke/bo...

These triangles are known to have a periodic billiard path: (1) All acute triangles. (2) All right triangles. (3) All rational triangles. (4) All obtuse triangles with obtuse angle smaller than 5 pi/8 (the 112.4 deg that I quoted). #MathSky #Mathematics #Geometry #Billiards

Sharp eyes to notice the two perpendicular bounces. Probably not for all triangles, I agree.

Beautiful indeed. And with recent results from the study of translation surfaces.

Sure. Have them email me, [email protected].

See also: "Why can't a nonabelian group be 75% abelian?" mathoverflow.net/q/211159/6094

I wonder in which dimensions is the cylinder/sphere volume ratio rational?
#Mathematics #MathSky #Geometry

p.4 of their paper details the construction. "the Noperthedron has 3·30=90 vertices." They set three pts C1,C2,C3 and then apply the cyclic group C_30 to each.

The Rupert property requires the convex polyhedron P to tunnel by translation through an isometric copy of P. I wonder if twisting while translating would permit any P---even the "Noperthedron"---to pass through itself? #Mathematics #Geometry #MathSky

Yes, the authors clearly had fun! :-)