How penguins see the world

Sometimes, shifting our view is the key to seeing things more clearly.
This quincuncial Antarctic-centered projection offers a fresh take on the South Pole, allowing us to appreciate Antarctica from a different perspective, as well as the vastness of the world’s oceans.

Read more about quincuncial maps.

“The World on a Quincuncial Projection”, from Peirce (1879) – Available as prints.

World Map on a Dodecahedron

With the holiday season approaching, here’s a fun and educational activity to enjoy with your kids. Assemble a three-dimensional world map by cutting and folding a single-piece dodecahedron template featuring a gnomonic projection by Carlos A. Furuti.
Download the PDF template here.
A simple and creative way to explore geography while spending quality time together.

Voyage au centre de la géométrie

Voyage au centre de la géométrie” est une rubrique emblématique que nous avons eu le plaisir de tenir pendant de nombreuses années dans la célèbre revue suisse ‘Mathécole‘. Très appréciée des enseignants et du grand public, cette rubrique visait à rendre les mathématiques accessibles et fascinantes pour tous.

Bien que Mathécole, un puissant outil de diffusion des mathématiques, ne soit plus publié, vous pouvez encore consulter ou télécharger gratuitement certains numéros contenant nos articles via les archives en ligne. Nous vous invitons à les explorer et à redécouvrir la richesse de ces contenus :

· Le puzzle outil didactique 1: #173,

· Le puzzle outil didactique 2: #177,

· Le puzzle outil didactique 3: #179,

· Découper, assembler, comprendre: #183,

· Métamorphoses géométriques: #184,

· La courbe dans tous ses états: #189,

· Parcours et détours: #196.

Ces archives témoignent de l’importance de Mathécole dans la vulgarisation des mathématiques et de son impact durable. N’hésitez pas à parcourir ces articles pour en apprendre davantage et pour vous en inspirer !

Useful Topology

In this video, a practical application of topology is presented through a simple knot technique for styling plant pots. This method transforms standard planters into trendy hanging displays.

The Intrigue of Simplicity

“A world without problems is an illusion, so is a world without solutions.” – Gianni A. Sarcone

According to the second rule of Sarcone & Waeber’s puzzle-solving principles, “nothing is ever as simple as it seems.” This is why we enjoy deceptively simple puzzles that seem almost impossible to solve. Here’s a classic topological puzzle you can create and enjoy with your kids.

You can explore the full set of puzzle-solving rules by Sarcone & Waeber here: https://www.archimedes-lab.org/sarcone_rules.html

Exploring Impossible Figures: A Philosophical Twist on Reality

Impossible figures are intriguing forms that defy the reality of our 3D world. In the 90s, I began experimenting with representations of cylinders featuring fictitious right angles—an artistic play on geometry. These twisting impossible figures, which defy mathematics and physics, are ideal for interior decoration or merchandise like t-shirts or mugs because they captivate the viewer’s imagination and provoke thought. Their striking, paradoxical nature draws attention, making them perfect conversation pieces, while also offering a philosophical twist on the idea that what seems real may not always be.

By stripping those imaginary geometric form down to their essence, I instill them with greater power.

These drawings are taken from my book Drawing Optical Illusions, still available on Amazon.

And are available as prints and t-shirts and merch from my online gallery!

Buy prints and apparels here: https://redbubble.com/shop/ap/164384901
Buy prints and apparels here: https://redbubble.com/shop/ap/164477598
Buy prints and apparels here: https://redbubble.com/shop/ap/164403619

Impossible Escape: A Topological Illusion

This is a fun and surprising escape trick for kids and family, that uses simple props:

· 1 karabiner clip,

· 1 metal ring,

· 1 loop of cord.

To begin:

1. The ring and the green karabiner clip are securely attached to the cord and cannot be removed.

2. Now, watch closely as I attach the green karabiner to the metal ring, making the setup even more complex.

3. Surprisingly, I can now simply pull the cord free.

Can you believe your eyes? Let’s try it together!

More topological magic tricks:

https://archimedes-lab.org/2021/06/29/magic-topology-2/

https://archimedes-lab.org/2020/06/09/magic-topology/

https://archimedes-lab.org/2017/12/14/how-to-magically-untie-a-shoelace-double-knot/

Magic Square for Gunners

A magic square is a grid where the sum of the numbers in each row, column, and diagonal is the same, creating a harmonious balance. A “geomagic” square, on the other hand, is a grid of geometrical shapes where each row, column, or diagonal can be assembled into an identical shape known as the “target shape”. Like numerical magic squares, all shapes in a geomagic square must be distinct.

Concept by Lee Sallows.

The postage stamp below, issued by Macau Post on October 9, 2014, pays tribute to Lee Sallows, the creator of geomagic squares.

Further reading.