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Midpoints of a quadrilateral form a parallelogram

Take any quadrilateral, like this one then mark the midpoints, and connect them up. It sure looks like a parallelogram, doesn’t it? The amazing fact here is that no matter what quadrilateral you start with, you always get a parallelogram when you connect the midpoints. This is the kind of result that seems both random and astonishing. You have to …

Beautiful Mathematics

“Beauty is the first test: there is no permanent place in the world for ugly mathematics.” – G. H. Hardy I’ve been reading Proofs from THE BOOK  by Aigner and Ziegler, a paean to beautiful mathematics. The Book refers to a conceit of the mathematician Paul Erdős. From wikipedia: [Erdős] spoke of “The Book”, an imaginary book in which God …