"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This ...

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 ...

Two years ago, a couple of high school classmates each composed a mathematical marvel, a trigonometric proof of the Pythagorean theorem. Now, they’re unveiling 10 more. For over 2,000 years, such ...

When a shape is enlarged, the image is similar to the original shape. It is the same shape but a different size. These two shapes are similar as they are both rectangles but one is an enlargement of ...