Arithmetic

Multiplications—for a change! | Tangente

The world of magic squares is still very much alive and remains an active field of research. Access to computing power has rekindled enthusiasts’ interest in these arithmetical objects. What happens if we try to define a multiplicative form of magic?

Conway's sequences and conjectures | Tangente

Conway loved playing with number sequences. His explorations led him to formulate conjectures that are elementary to state but formidable to tackle.

Jumps in number sequences | Tangente

By playing with letters, digits and numbers, we can build sequences whose "stop" and "restart" rules reveal surprising arithmetic phenomena. It would take a clever mind indeed to fathom the jumps between successive terms!

Welcome to 2020! | Tangente

As usual, the new year inspired the Tangente team and their friends, who all vied with one another to tease out the number 2020's astonishing properties.

Divide and conquer: divisibility tests in action | Tangente

Many arithmetic problems can be solved using standard methods, whether elementary or advanced. But some puzzles call for a basic concept—divisibility—and a little ingenuity.

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.

Base 60 still dictates our schedules | Tangente

The revolutionaries introduced the decimal system for weights and measures, and despite a few Anglo-Saxon holdouts, it prevailed across the globe. Yet bases 12 and 60 live on, notably in the measurement of angles and the passage of time…

Counting without counting | Tangente

Everyday language still bears traces of certain ancient counting practices.

Two numeral systems you were spared | Tangente

Numeral systems are a matter of conventions dictated by history and efficiency. But what if...

Writing large numbers: not so simple! | Tangente

Even with a positional decimal system, not everyone writes large numbers in the same way.

Pre-Columbian numeral systems | Tangente

In which we discover that South American civilizations did not wait for Christopher Columbus before adopting numeral systems

Mental arithmetic: tips, games and educational challenges

A mass-circulation weekly takes a look at mental arithmetic!

Breaking the ADFGVX cipher in 1914–18

For the second phase of the German spring offensives of 1918, the Germans added the letter V to the ADFGX cipher. But Georges Painvin broke the new cipher within hours… paving the way for final victory. The new system, though apparently more sophisticated, was actually weaker!

Crop circles and mathematics: Fibonacci in the fields

Another form of optical art is found in the famous crop circles, or "crop formations" (technically known as agroglyphs). These geometric patterns, most often created in cereal fields, range in size from a few square metres to several hectares. They are made by cutting, twisting or bending stalks of grain, usually at night and in record time.

Fibonacci in concrete art: mathematics and aesthetics

The famous Fibonacci sequence begins 1, 1, 2… and each term is the sum of the previous two. It abounds in surprising properties. Has it finally yielded all its secrets? That remains a mystery, as some artists are now working with it and exploring it from every angle.

Codebreaking in intelligence: history and methods

Throughout history, decrypting coded messages has played a major—though often overlooked—role. From the first battle won through cryptography alone to the breaking of Enigma, examples abound, but they have often been kept hidden. That remains true today.

Tangente's 30th anniversary program | Tangente Magazine

Here is the programme (which will be updated regularly) for Tangente's 30th anniversary celebrations at the Musée des arts et métiers on Sunday, December 3, 2017. Admission is free for everyone!

The Ramanujan–Hardy duo on screen | Tangente Magazine

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.

The mysteries of the Ishango bone | Tangente Magazine

The mysterious Ishango bone has not yet given up all its secrets