Inspiring and Creative Resources & Tutorials for Science-Curious People
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.
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” 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 !
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:
This innovation could redefine memory and computation, shaping the future of electronics.
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!
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.
Paper wasps (Polyistes dominula) stand on the water’s surface while drinking. The ‘surface tension‘ of the water, a property that causes water molecules to stick together, acts like an elastic sheet, supporting the wasp’s weight. The wasp’s six legs create depressions in the surface, forming lens-like curvatures that cast tiny shadows beneath the water. Surface tension is crucial for many organisms, as it creates a habitat for various life forms on the water’s surface.
surface-tension-formula
In this formula, surface tension (γ) represents the force across an imaginary line divided by twice the length of that line. The factor of 2 is essential because, when splitting the surface of a bubble, we’re actually pulling apart molecules on two surfaces—the inner and the outer.
⇨ Read More.
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.
Does the color of wine change when poured into a glass?
Although it may appear darker, the red shade remains the same. This visual trick is a result of the Munker-White illusion—where our brain perceives colors differently depending on their surrounding context.
If you’re intrigued by puzzles like this, reach out to my syndication agent to feature them in your publication.
This op art piece is also available as prints and canvases in our online gallery.
A golden ellipse is one where the axes are in golden proportion, meaning the ratio of the major axis (a) to the minor axis (b) is the golden ratio:
φ = (1 + √5)/2.
To visualize this, draw a golden ellipse along with its inscribed and circumscribed circles: the smallest circle fitting inside the ellipse and the largest circle surrounding it.
Interestingly, the area of the ellipse matches the area of the “annulus” formed between these two circles!
Here’s how it works:
Let a be the semi-major axis and b the semi-minor axis, with a = φb.
The area of the annulus is:
π(a² − b²) = πb²(φ² − 1)
The area of the ellipse is:
πab = πφb²
And as φ² − 1 = φ, then πb²(φ² − 1) = πφb².
Isn’t it fascinating how geometry intertwines with the golden ratio?
