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 ...
In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...
Take any quadrilateral such as ABCD above. Construct the midpoints of each side and join them to form another quadrilateral EFGH. Varignon's Theorem asserts that the ...
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