Math for everyone
Mathematical content accessible to everyone
Signature and the tiling theorem | Tangente
Have you ever noticed? In friezes, tilings and other periodic patterns that repeat or exhibit symmetries, the artist's range of possibilities is actually quite limited. A fundamental theorem provides a complete enumeration of these patterns.
The world of puzzlers 3 | Tangente
The small world of puzzle enthusiasts, collectors and puzzle makers is astonishingly diverse. It includes specialists in tilings and elegant dissections.
The secret of patterns in the Islamic world
The tilings and interlaced designs of medieval Islamic art command our admiration. But could a few simple geometric shapes lie behind this apparent complexity of line segments, interlacing, nested curves and polygons?
A first overview
Tiling began as a practical idea. Roads and houses were paved long before anyone saw mathematics in them! Since then, the concept has been extended, and today even non-Euclidean and four-dimensional spaces are tiled…
The art of Harry Lindgren | Tangente
A math enthusiast passionate about geometric dissections introduced powerful methods that remain classics today.
Proofs without words
Proofs without words are figures that visually illustrate algebraic relations, some of them fairly complex.
The world of "puzzlers" 2 | Tangente
Among the best-known mechanical puzzles are wooden knot puzzles, which the American Bill Cutler analyzed scientifically.
Squaring the square | Tangente
The search for perfect squared squares has inspired many attempts, some of them very elegant.
Dissecting the square, from Abu al-Wafa to Dudeney
Cutting a given square into identical squares seems easy at first glance—and produces beautiful mosaics. But is it really that simple? What if, instead of identical squares, we require them all to be different, creating ingenious puzzles? A rich geometric world opens up…
Four authors for one theorem | Tangente
A tangram consists of seven polygonal pieces that can be assembled to form a given shape. But what about the inverse problem? When can two figures be solutions to the same puzzle? When do they admit the same dissection into elementary shapes? A famous theorem answers that question completely.
The geometry of scissors
Dissections are an inexhaustible source of research, discoveries and feats for amateur geometers and seasoned mathematicians alike. Born of practical concerns, they have become a treasure trove of mathematical recreations and brainteasers.
Pentominoes | Tangente
Let's rediscover pentominoes and the countless problems they generate
Stomachion: the world's oldest puzzle | Tangente
The Stomachion is certainly the world's oldest puzzle. It owes its fame not only to Archimedes' interest in it, but also to the extraordinary circumstances in which the Syracusan's writings, lost for two thousand years, were recovered…
The world of "puzzlers" 1 | Tangente
Cuts, dissections and cunning assemblies give rise to extraordinary mechanical puzzles. A remarkable annual convention is devoted to them.
Paradoxes in the world of dissections | Tangente
Tilings and geometric dissections gave rise to equidissection puzzles, which have kept our brains buzzing since the 18th century.
Mathematical calligrams | Tangente Magazine
A calligram is a poem arranged on the page to form an image, usually related to its subject. Here we present several quotations about mathematics in the form of calligrams.
Poets talk to us about math… and vice versa
Mathematics and poetry are two ways of making sense of the world. Worlds apart? Not quite.
Holiday geometry | Tangente Magazine
The holidays are also a chance to uncover the mathematics all around us
Raymond Smullyan (1919–2017): logician and magician
An eclectic mathematician, Raymond Smullyan, who died last June, was best known to the general public for his books of mathematical recreations centered on logic.
The mysteries of the Ishango bone | Tangente Magazine
The mysterious Ishango bone has not yet given up all its secrets