Amazing Math
Surprising or counterintuitive mathematical results and proofs
Jean Bourgain, exceptional Fields medallist | Tangente
The prodigious Belgian mathematician Jean Bourgain (1954–2018) worked in many fields of mathematics, forging wholly unexpected links between seemingly separate areas. His outstanding results earned him numerous awards.
A free ticket to the stars: Newton | Tangente
How far we have come since Newton's famous apple! Recently discovered remarkable properties of the gravitational field raise the prospect of space missions requiring almost no energy—not only to the Moon, but to other planets as well…
Breakthrough in quasi-linear multiplication | Tangente
Multiplying two integers dates back several thousand years. In 2019, at last, the algorithm was improved!
Operations in billiards
One of the arts and pleasures of mathematics is finding different ways to represent problems. Some problems in dynamics can profitably be replaced by the study of trajectories on a billiard table, revealing hidden structures—and hence hidden logical beauty.
In search of the missing squares | Tangente
There is no need to invoke the paradoxes of infinity to have fun with areas: a simple rectangle is enough to create some formidable puzzles! All you need is a sheet of paper, some pencils, a ruler and a pair of scissors—and you are ready to make little squares disappear.
Remarkable mathematical surfaces | Tangente
Ruled surfaces in architecture | Tangente
How can a surface made up of straight lines be curved? That is the paradox of ruled surfaces!
Telepathy
How can we be sure that the predictions made are not the result of a gift of clairvoyance? Profound results in probability, which sometimes seem counterintuitive, can help convince you that the results observed are in fact nothing out of the ordinary...
A mathematical approach to the paranormal
When it comes to the paranormal, it may seem easy to separate fact from fiction and use various tests and experiments to prove that a supposed medium or clairvoyant is nothing of the kind. Not so fast! Such protocols are difficult to set up, and few impressionable souls know about the Yule–Simpson paradox...
Play with 2019: curiosities and decompositions | Tangente
We thought 2019 was an unremarkable number. Not at all! As it does every year, the Tangente team has surpassed itself in uncovering its finer qualities.
Mathematics lends itself to play
Play does not seem more closely linked to one discipline than another. Yet mathematics and play enjoy a special relationship. Mathematics lends itself remarkably well to play, and play returns the favour.
The mind-bending properties of infinity
Infinity abounds in paradoxes of every kind. For example, the terms of certain numerical series can be rearranged so that they converge… to any number chosen in advance! Skeptical? Follow Bernhard Riemann's reasoning…
Combinatorics, past and present: An interview with Pierre Duchet
The study of combinatorial structures is a recent branch of mathematics, rich in counting problems. A journey into a far too little-known realm.
Having fun with the number 60 | Tangente
Although 60 is no longer the retirement age, there are still plenty of opportunities to play with the number 60.
Untangling the mysteries of rubbery deformations
The metric properties of modelling-clay objects change when they are deformed. Other properties, known as topological properties, remain unchanged. Surprisingly, algebra enters the picture. This naturally leads us to consider knots and the constituent molecules of DNA.
Ethical driving - mathematics brief | Tangente
Programming self-driving cars raises ethical questions. Unexpected new conundrums have emerged. Some require only minor adjustments, but others remain unsolvable for now.
Reasoning means solving
Reasoning means organizing your thoughts. Yes, but how? Are there methods for keeping our thoughts from descending into anarchy and confusion? Mathematics is, by its very nature, the discipline that has enabled us to answer these questions over the centuries. And it works!
Elementary yet powerful: the pigeonhole principle
If your chest of drawers has two drawers and you put three items of clothing in them, at least two items—possibly all three—must end up in the same drawer. This seemingly trivial observation is actually the basis of a powerful reasoning tool!
Build your mysterious crystal: patterns & assembly | Tangente
The Mysterious crystal—actually the first stellation of the rhombic dodecahedron—can be built from six identical pieces. Whether you use scissors, a cutting machine or a 3D printer, choose whichever method suits you. The hardest part is working out how to assemble them.
The mysterious crystal
For a change, beneath its polyhedral exterior, the subject of this instalment in our mathematical objects saga is a puzzle. You will find everything you need to build it on the Tangente website.