Cut-the-Knot (CTK) is a free, advertisement-funded educational
website which Bogomolny maintained from 1996 to 2018. It is devoted to popular exposition of various topics in
mathematics. The site was designed for teachers, children and parents, and anyone else curious about mathematics, with an eye to educating, encouraging interest, and provoking curiosity. Its name is a reference to the legend of
Alexander the Great's solution to the
Gordian knot. CTK won more than 20 awards from scientific and educational publications, including a
Scientific American Web Award in 2003, the
Encyclopædia Britannicas Internet Guide Award, and
Sciences NetWatch award. The site contains extensive analysis of many of the classic problems in
recreational mathematics including the
Apollonian gasket,
Napoleon's theorem,
logarithmic spirals, the "Futurama Theorem" from the episode "
The Prisoner of Benda", the
Pitot theorem, and
the monkey and the coconuts problem. One page includes 122 proofs of the
Pythagorean theorem. Bogomolny wrote a manifesto for CTK in which he said that "Judging Mathematics by its pragmatic value is like judging symphony by the weight of its score." He described the site as "a resource that would help learn, if not math itself, then, at least, ways to appreciate its beauty," and he wondered why it is acceptable among otherwise well-educated people "to confess a dislike and misunderstanding of Mathematics as a whole." Many mathematical ideas were originally illustrated by
Java applets, but most were later replaced by
GeoGebra applications, also used for material added later. CTK wiki (powered by
PmWiki) extends the main site with additional mathematical content, especially that with more complicated formulae than available on the main site. From 2001–2004 several CTK articles with interactive applets were also hosted as a column at the
Mathematical Association of America website. ==Book==