Mathematicians Discover New Shapes to Solve Decades-Old Geometry Problem

Mathematicians have solved a long-standing problem about "shapes of constant width" in higher dimensions. A team of five researchers developed a simple method to construct constant-width bodies in any dimension that are exponentially smaller than a ball. Their algorithm creates n-dimensional shapes with volumes at most 0.9^n times that of a ball.

This breakthrough answers a question posed in 1988 and provides insight into higher-dimensional geometric shapes. The construction may have applications in machine