Which lock opens the gate?
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 !
Memristor: Memory in Electronics
In 1971, Leon Chua proposed the “memristor,” a groundbreaking component that “remembers” past electrical states by adjusting its resistance based on charge flow. Unlike conventional resistors, it retains information even without power.
In 2008, HP Labs confirmed its existence, marking a milestone in nanoelectronics. Memristors hold promise for:
- Energy Efficiency: Retaining memory without power, eliminating boot-up delays.
- Neuromorphic Computing: Emulating synaptic behavior for AI and neural networks.
This innovation could redefine memory and computation, shaping the future of electronics.
Bullets vs. Water: The Physics of Drag Force in Action
Ever wondered what happens when you shoot a bullet in water?
The deeper the water, the faster the bullet slows down. Water’s higher density causes much more resistance than air, rapidly draining the bullet’s kinetic energy. In just a few meters, the bullet can come to a complete stop!
Why? Water creates a drag force that decelerates the bullet. The formula behind this?
Drag Force (Fₑ) = ½ * Cₔ * ρ * A * v²
Where:
Cₔ = Drag coefficient (depends on the bullet shape)
ρ = Water’s density (about 1000 kg/m³)
A = Bullet’s cross-sectional area
v = Bullet’s velocity
As the bullet travels, drag slows it down and uses up its energy quickly. In just a few meters, the bullet is stopped dead in its tracks!
Visual Math Challenge: Rectangle in an Octagon
One fascinating property of a rectangle inscribed in an octagon is that its side ratio aligns perfectly with the “silver ratio“, or 1+√2. But there’s more to discover! Without doing any calculations, can you prove that the area of this gray rectangle is exactly half of the full octagon’s area? Give it a try!
The “silver ratio” is connected to various mathematical concepts, such as Pell numbers and continued fractions. It serves as the limiting ratio of consecutive Pell numbers, similar to how the golden ratio relates to Fibonacci numbers.
