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, jorourke@smith.edu.

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! :-)

*Visual Complex Analysis* by Tristan Needham. global.oup.com/academic/pro...

Henry Cohn figured that out: Again, not the cube:
mathoverflow.net/a/73941/6094