“Da Ya Think I Am √(1 + tan²c)?”
– Rod Stewart
A bit of lightness in the world of math goes a long way, especially when it comes to mnemonics. After all, a little humor and creative wordplay never hurt anyone.
Humor & Trigonometry
Neuberg’s Theorem
A captivating result from geometry:
- Construct squares outwardly on the sides of triangle △ABC.
- Use the centers O1, O2, O3 of these squares to form a new triangle.
- Next, construct squares inwardly on the sides of this new triangle.
The surprising outcome? The centers of these inward squares will perfectly coincide with the midpoints I1, I2, and I3 of the sides of the original triangle △ABC.
For a deeper dive into the proof, check out this resource:
Neuberg’s Theorem – Detailed Explanation.
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.
Multiple Lock Puzzle
32, numerical ambigram
Here’s our first ambigram of the year: 32 = 99 – 1 – 66. This arithmetic equation holds even when you flip the image below upside down! The next step is to do the same with the number 23 — any ideas?
⇨ More number facts.
2025
The Cyanometer: A Tool to Measure the Sky’s Blueness
In the 18th century, Swiss scientist Horace-Bénédict de Saussure invented the “cyanometer,” a simple yet poetic device— a circular chart with 52 shades of blue, ranging from white to dark blue, to measure the sky’s blue hues. Inspired by his love for the Alps, especially Mont Blanc, Saussure climbed to great heights to study the deeper blue skies at higher altitudes.
Saussure believed the sky’s color was influenced by atmospheric particles. He tested the cyanometer at different elevations, noting that the summit of Mont Blanc matched the 39th shade. Later, explorer Alexander von Humboldt set a new record of 46 during his Andean expeditions.
Although Saussure’s theory linking sky color to atmospheric moisture didn’t pan out, his invention captured imaginations. Though it faded from science, the cyanometer lives on as an artistic and symbolic nod to our curiosity about nature. Modern versions even track air quality while celebrating the beauty of the ever-changing sky.
Next time you look up, think of Saussure and his ingenious little tool!
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.
The Largest Probable Prime Made of 1’s
Did you know the largest known repunit probable prime has over 8 million digits—and every single one is a “1”?
This incredible number, called R₈,₁₇₇,₂₀₇, is written as:
(10⁸¹⁷⁷²⁰⁷ − 1) ÷ 9
It’s a record-breaking giant in number theory, with 8,177,207 consecutive “1”s.
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 !
