Posts

Posted on

The Two Faces of a Spoon

At Archimedes’ Lab, we love discovering how even the most ordinary objects can reveal extraordinary truths. Take a spoon—yes, just a regular kitchen spoon. Hold it up and take a look… Why is your reflection upside-down on one side, and upright on the other?

That’s not magic—it’s optics! The concave side (the scooping part) acts like a converging lens with a focal point. When your face is close enough, the reflected light rays cross at that point, flipping your image. Voilà—an upside-down version of you. Now flip to the convex side, and your image stays upright, just a little smaller and bent around the edges.

During our workshops, we like to turn this into a playful moment. We joke with kids that the spoon is magical—it reveals who’s telling the truth. “If your face is upside-down,” we say with a grin, “the spoon knows you’re fibbing!” The reaction? Giggles, wide eyes, and just the right moment to sneak in a quick optics lesson.

One humble spoon. Two faces. A world of curious learning.

Reflections on a spoon
Posted on

Hands-On Wonders: A Mathemagical Collection

Ever wondered what happens when math puts on a magician’s hat? These books are the distilled magic of my hands-on math workshops across Europe — from Paris to Palermo, Geneva to Ghent — where paper folded, minds twisted, and logic sparkled in English, French, and Italian!

Impossible Folding Puzzles

1) “Impossible Folding Puzzles and Other Mathematical Paradoxes” — a playful dive into mind-bending problems where nothing is quite what it seems. Can a puzzle have no solution… or too many? Dare to fold your brain.

Still available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — where math meets illusion to spark curiosity and creativity.
Perfect for teachers, students, and curious minds: touch, fold, cut… and let the magic unfold!
Available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — un livre où maths et illusion se rencontrent pour éveiller curiosité et créativité.
Pour enseignants, élèves et esprits joueurs : touchez, pliez, découpez… la magie opère!
Dispo sur Amazon.

Pliage decoupages

3) “MateMagica” —  They say there’s enough carbon in the human body to make 900 pencils… but just one is all you need for these clever puzzles!
Fun, surprising, and thought-provoking — because, as Martin Gardner put it, “Mathematics is just the solution of a puzzle.”
Now on Amazon.

3) “MateMagica” —  Si dice che nel corpo umano ci sia abbastanza carbonio per 900 matite… ma per questi rompicapi ne basta una!
Sorprendenti, divertenti e stimolanti — perché, come diceva Martin Gardner, “la matematica è nient’altro che la soluzione di un rompicapo.”
Disponibile su Amazon.

I write and illustrate my own books in five languages: English, French, Italian, German, and Spanish.
If you’re a publisher or literary agent seeking original, high-quality educational content that blends creativity with clarity, I’d be pleased to explore potential collaborations.

Posted on

Wittenbauer’s Parallelogram

Try this fascinating geometric construction:
Draw any quadrilateral—no need for precision. Divide each side into three equal parts. At each vertex, connect and extend the two trisection points nearest to it on the adjacent sides. Once you’ve completed this for all four vertices, you’ll find a perfect parallelogram nestled within your original shape.

Wittenbauer’s Parallelogram

This elegant result was discovered by Austrian engineer Ferdinand Wittenbauer.

Posted on

Hidden in Plain Sight


Many prey animals, like deer and wild boars (ungulates), are dichromats — they have only two types of cone cells, sensitive to:
• short wavelengths (blue)
• medium wavelengths (green)
They lack red-sensitive cones, so they can’t tell red or orange from green or brown.To their eyes, a tiger’s vivid orange coat blends seamlessly into the forest — it looks greenish or brownish, like the surrounding foliage.

tiger color camouflage

So, a tiger’s color isn’t designed to fool us — it’s meant to fool them.
To us, it’s a blazing orange predator.
To a deer, it’s a silent shadow in the grass.
Camouflage, it turns out, is all about who’s watching.

Further reading: https://www.archimedes-lab.org/what_is_seeing.html

Posted on

The Mitre Puzzle

A timeless geometric challenge by Sam Loyd…

The Mitre Puzzle is a classic dissection problem that asks: how can you cut a bishop’s mitre-shaped figure—a square with a triangular notch—into pieces that rearrange perfectly into a square?

Sam Loyd thought he had the answer with a four-piece solution. But there was a catch—his pieces actually formed a rectangle that just looked like a square. The illusion fooled many, but the puzzle wasn’t truly solved.

Enter Henry Dudeney, Loyd’s contemporary and fellow puzzle master. Dudeney showed a correct solution requiring five pieces, and for over a century, that was accepted as the minimal number needed.

Fast forward to 2024. Finnish mathematician Vesa Simonen shook things up by discovering several true four-piece solutions—finally cracking what was long considered impossible.

Mitre puzzle, Sam Loyd

It’s interesting how even the oldest puzzles can still surprise us when we look closer.

You can explore Vesa Timonen’s innovative four-piece solution to the “Mitre Puzzle” on his dedicated webpage.

If you want to dive into Sam Loyd’s original puzzles, you can grab his classic book here.

Posted on

Roman Numerals vs Hindu-Arabic Numbers in Psychology

What Our Brains See vs What They Read

The way our brain interprets Roman numerals and Hindu-Arabic numbers reveals an interesting distinction in psychology—especially when viewed through the lens of communication theory.

According to the psychologist and communication theorist Paul Watzlawick, signs and symbols can be divided into two categories: analogical and digital.

· Analogical signs resemble what they represent. They are intuitive and visually descriptive.

· Digital signs are symbolic. They rely on learned codes and have no visual connection to what they signify.

In this sense, Roman numerals (like I, II, III) are analogical. When we see “II”, we can immediately see two units. The visual repetition reflects the quantity directly—our brain interprets the number almost as a drawing of its value.

On the other hand, Hindu-Arabic numbers (like 2, 3, 4) are digital. The symbol “2” doesn’t visually resemble two objects—it’s abstract. Understanding it depends on prior learning and decoding. The brain treats it more like language than image.

This distinction matters. Roman numerals engage perception in a way that mimics reality. Arabic numerals, by contrast, engage abstract reasoning. The first shows, the second tells.

In daily life, we may not notice the difference—but psychologically, the visual nature of Roman numerals connects us to meaning more directly, while the efficiency of Arabic numerals supports speed, calculation, and abstraction.

In short:
Roman numerals speak to the eye.
Arabic numbers speak to the mind.

⇨ More about numbers.

roman numbers vs arabic numbers
Posted on

GHOST COLORS (2)

Take a closer look at the image below—you’re in for a mind-bending surprise! There’s absolutely NO yellow, and not even red or green in sight. (Zoom in if you don’t believe it!) The only actual colors used are blue, cyan, and magenta.
What you’re seeing is a fascinating phenomenon known as “simultaneous color contrast” and “color assimilation”.—effects that ‘trick’ the brain into perceiving colors that aren’t really there.

© Gianni A. Sarcone

When you magnify a portion of the image in Photoshop, as seen below, to the right, you see a series of black bars. Some gaps that appeared yellow at first are actually pure WHITE, and the eyedropper tool confirms that only CYAN and MAGENTA are present.

The green tint perceived in some areas is a result of the interaction between black and cyan, just as the appearance of red is due to the interplay of black and magenta. As for the yellow-looking circle, it’s actually an optical effect caused by the white space between the black bars reacting to the surrounding dark blue lines — a classic case of simultaneous contrast.

© GIanni A. Sarcone

⇨ Learn more.

Posted on

Assembly Fail: The Impossible Ikea Chair

Sometimes, following the instructions doesn’t lead to the expected result. This visual illusion explores how perception, logic, and a touch of ambiguity can turn a simple assembly into something entirely unexpected.

impossible chair
© 2002, Gianni A. Sarcone.

Now available on our Gallery shop—ideal for lovers of visual humor, design fails, and optical absurdities.

Posted on

Impossible rectangle?

Cut out the two identical, imperfect rectangles shown here—each missing two corners. Follow the lines to divide them into four geometric pieces… Then try to reassemble them into one perfect rectangle.

Sounds simple? Think again! Solve it? Tell us what made it such a brain-bender!

I’ve always had a passion for puzzles made of simple geometric pieces—especially those that seem almost impossible to solve despite the deceptively simple shapes and limited number of elements. As an Op Art artist, I find these visual enigmas a delight not only for the eye but also for the mind. For someone drawn to minimalism like me, beauty lies not just in pure form, rules, or apparent simplicity, but in the very intention of the game: to create something concrete and well-defined out of very little. And yet, at first glance, the pieces rarely seem to match the information at hand—as if something’s always missing, or as if the pieces resist aligning with your will.

Back in the ’80s, I created numerous puzzles with these paradoxical traits—some even became worldwide hits. When people would say, “Ah, so you’re the creator of that devilish puzzle?” I would always reply, “No, not a puzzle, but a piece of optical art.” Or: “No, not a puzzle, but a visual paradox.” Or sometimes: “No, not a puzzle, but a moment of zen-like reflection.”

No, I’ve never created puzzles—but rather works that turn geometry into visual meditation.

⇨ More visual enigmas to create.

Posted on

The Origins of Our Numerals

The Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī (كتاب الفصول في الحساب الهندي), or The Book of Chapters on Hindu Arithmetic, authored by Abū al-Ḥasan Aḥmad ibn Ibrāhīm al-Uqlīdisī in 952 CE, is the earliest known Arabic treatise detailing Indian arithmetic and the use of Hindu-Arabic numerals. A unique manuscript of this work is preserved in the Yeni Cami Library in Istanbul. The treatise also offers the earliest documentation of numerals in use in Damascus and Baghdad.

Another significant reference is found in Talqīḥ al-Afkār bi-Rusūm Ḥurūf al-Ghubār (تلقيح الأفكار برُسوم حروف الغبار), or Fertilization of Thoughts with the Help of Dust Letters, by the Berber mathematician Ibn al-Yāsamīn (ابن الياسمين), who died in 1204. In the excerpt shown below, he presents the Indian numerals, stating:​

“Know that specific forms have been chosen to represent all numbers; they are called ‘ghubār’ (dust), and they are these (first row). They may also appear like this (second row). However, among us, people use the first type of forms.”​

An intriguing anecdote about Ibn al-Yāsamīn is that he composed mathematical poems, such as the Urjūza fī al-Jabr wa al-Muqābala, to make algebra more accessible. These poetic works were not only educational tools but also reflected the rich interplay between mathematics and literature in the Islamic Golden Age.