path 16+16n bytes Closed path (similar to polygon) ((x1,y1),...) path 16+16n bytes Open path [(x1,y1),...] polygon 40+16n bytes Polygon (similar to closed path) ((x1 ...

The shapes could be defined by polynomials — equations from high school math that sum up sequences of terms. But these were special polynomials, the group realized, in that they corresponded to curves ...

Chatbots like ChatGPT get stuff wrong. But researchers are building new A.I. systems that can verify their own math — and maybe more. By Cade Metz Reporting from San Francisco On a recent ...

Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer. In 1986, after the space shuttle Challenger ...