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 ...

Dive into one of the most wicked geometry problems and see it explained step by step in a clear, intuitive way. This lesson ...

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 ...

An AI from Google DeepMind can solve some International Mathematical Olympiad (IMO) questions on geometry almost as well as the best human contestants. How does ChatGPT work and do AI-powered chatbots ...

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 ...

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 ...

A system developed by Google’s DeepMind has set a new record for AI performance on geometry problems. DeepMind’s AlphaGeometry managed to solve 25 of the 30 geometry problems drawn from the ...

This geometry challenge puts your spatial reasoning and problem-solving skills to the test as you work to find the area using given clues and relationships. The explanation breaks the problem down ...

Mathematics of Operations Research, Vol. 34, No. 4 (Nov., 2009), pp. 869-879 (11 pages) Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation ...