Mathematicians Solve Centuries-Old Geometry Problem: First Convex Polyhedron That Cannot Pass Through Itself
By
fleahunter
Crackling crust, pillowy middle. The kind of bagel that earns a second cup of coffee.
Summary
Mathematicians have solved a centuries-old geometry problem about whether a shape can pass through a hole in a copy of itself. The research identifies the first known convex polyhedron that cannot pass through a hole in an identical copy, solving a problem that originated with a 17th-century royal bet between King Frederick William I of Prussia and the mathematician Leonhard Euler. The solution involves complex mathematical analysis of convex polyhedra and their ability to pass through tunnels in identical shapes.
Key quotes
· 4 pulledThe full menagerie of shapes is too diverse to get a handle on, so mathematicians tend to focus on convex polyhedra: shapes, like the cube, that have flat sides and no protrusions or indentations.
When such a shape is much wider in some directions than others, it's usually easy to find a straight tunnel that will allow another copy of the shape to pass through.
But many famous convex polyhedra — for instance the dodecahedron, or the truncated icosahedron...
After more than three centuries, a geometry problem that originated with a royal bet has been solved.
You might also wanna read
Understanding Mathematical Manifolds: From Riemann's Concept to Modern Geometry
The article explains the mathematical concept of manifolds, which are shapes that appear flat locally but may have complex global structures
quantamagazine.org·6mo ago
Mathematicians Prove Existence of Polyhedron Without Rupert's Property
Researchers Steininger and Yurkevich have proven the existence of a convex polyhedron that cannot have a hole cut through it large enough to
johncarlosbaez.wordpress.com·9mo ago
A visual introduction to differential geometry and Maxwell's equations through pictures
This article presents a pictorial introduction to differential geometry, aimed at making the mathematical foundation accessible to pre-unive
arxiv.org·22h ago
Mathematical Model Identifies the Optimal Threshold for Human Ambition
A collaborative mathematical study reconciled conflicting pieces of cultural advice by mapping the exact parameters of human ambition. Using
neurosciencenews.com·22h ago
Weak and Block-Equitable Colourings in Uniform Group Divisible Designs and Maximum Packings
This article presents a mathematical study of colourings in uniform group divisible designs and maximum packings. It defines weak c-colourin
doi.org·4d agoVC Dimension and the Fundamental Theorem of Statistical Learning: A Complete Mathematical Derivation
This article explains the theoretical foundations of statistical learning theory, specifically addressing when learning from data is guarant