Engineers use psychology, physics, and geometry to make robots more intelligent
The self-supervised learning framework Columbia Engineers call DextAIRity learns to…
Browsing Tag
geometry
‘Nasty’ Geometry Breaks a Decades-Old Tiling Conjecture
One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time.Since antiquity, artists and geometers…
The Fibonacci Numbers Hiding in Strange Spaces
McDuff and Schlenk had been trying to figure out when they could fit a symplectic ellipsoid—an elongated blob—inside a ball. This type of problem, known as…
New method to determine the dimensionality of complex networks through hyperbolic geometry
In the study, the similarity and popularity variables are combined to give rise to…
The New Math of Wrinkling Patterns
A few minutes into a 2018 talk at the University of Michigan, Ian Tobasco picked up a large piece of paper and crumpled it into a seemingly disordered ball…
Hypergraphs Reveal a Solution to a 50-Year-Old Problem
The goal here is to trace out triangles on top of these lines such that the triangles satisfy two requirements: First, no two triangles share an edge.…
Mathematicians Transcend a Geometric Theory of Motion
“ homology theory depends only on the topology of your manifold. is Floer’s incredible insight,” said Agustin Moreno of the Institute for Advanced…
A Father-Son Team Solves a Geometry Problem With Infinite Folds
After their 2015 success, the researchers set out to use their flattening technique to address all finite polyhedra. This change made the problem far more…
Is Geometry a Language That Only Humans Know?
Probing further, the researchers tried to replicate the performance of humans and baboons with artificial intelligence, using neural-network models that are…
A Mathematician Answers a 150-Year-Old Chess Problem
If you have a few chess sets at home, try the following exercise: Arrange eight queens on a board so that none of them are attacking each other. If you…