DeepMind, the Google AI R&D lab, believes that the key to more capable AI systems might lie in uncovering new ways to solve challenging geometry problems. To that end, DeepMind today unveiled ...

Explore area with partially tiled rectangles. Discover units used to measure area. Explore area with partially tiled rectangles. Can you apply what you know about multiplication to figure out the area ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an ...

The International Mathematical Olympiad (IMO) is a prestigious competition featuring talented high school students from around the world, in which competitors solve complicated mathematical problems.

An artificial-intelligence (AI) tool can rigorously prove whether geometric facts — statements about two-dimensional shapes such as triangles or polygons — are true, just as well as competitors in the ...

For over 150 years, a rule of thumb dating back to the French mathematician Pierre Ossian Bonnet has been accepted in surface theory: If the metric and mean curvature of a compact surface are known at ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. By wiggling a needle around while spinning it, you can minimize the amount of space it moves through, ...

Computers are working to solve an age-old geometry problem. Humans can’t “square the circle” by hand, which was proven in the 1800s. Computer solutions involve infinity, complexity, and some ...

Combinatorial geometry and density problems form a dynamic field at the intersection of discrete mathematics and geometric analysis. Research in this area explores the intricate arrangements of points ...