Mathematicians Reinvent the Wheel in Higher Dimensions to Solve Decades-Old Geometry Problem

Mathematicians have created a new family of shapes, similar to a multidimensional guitar pick, that roll like a wheel in higher dimensions. Wheels and spheres roll smoothly without wobbling because they are objects with constant width. In two and three dimensions, mathematicians have previously created smaller rolling objects called Reuleaux triangles and Meissner bodies — both similar in shape to guitar picks — that have constant width but less volume than wheels and spheres. Now a concise three-page proof offers a solution for higher dimensions.