Jean-Jacques Dupas

When polyhedra come in pairs

Swapping the faces and vertices of a polyhedron produces a new one, which can be built using elementary geometric constructions. This phenomenon once again demonstrates the close connection between arithmetic and geometry.

Cosmology and polyhedra

Regular polyhedra appear in many theories. These five solids fascinate us with their remarkable symmetries.

The astrolabe: all the answers

After reading the article on the planispheric astrolabe, practise using it by answering these questions

Magnus Wenninger, the "pope" of polyhedra

Building polyhedra is said to require the patience of a monk. Fittingly, the 20th century's greatest polyhedron builder was a Benedictine: Magnus Wenninger died in 2017 after a very long life devoted to God and geometry.

Remarkable surfaces

The planispheric astrolabe

The astrolabe is the scientific instrument par excellence! The king of measuring instruments, it ruled supreme for more than a thousand years. It has since lost its former glory, and few people still use it or handle it with nostalgia. Yet it offers a wonderful opportunity to put mathematics into practice.

A master of polyhedra!

Leonardo da Vinci studied mathematics with Luca Pacioli, the greatest mathematician of the age. But the pupil soon surpassed the master! The artist-geometer's depictions of polyhedron nets upend some firmly held beliefs about the Renaissance.

Applications of the second derivative

The concept of acceleration corresponds to a second derivative. It therefore seems only natural that a mathematical concept as sophisticated as the derivative should have concrete applications. Such applications arise in questions involving the profiles of roads and railway tracks.

A controversy over gears

What shape should gear teeth have to get the most out of gears? The question preoccupied 17th-century scholars so intensely that tempers sometimes flared. Philippe de La Hire and Gottfried Wilhelm Leibniz were two of the protagonists in this historic scientific dispute.

A new kind of calculator

The French company Numworks has joined the select club of calculator manufacturers. This new machine is based on open-source principles.

Build your Mysterious crystal

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.