Category: Perception

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The Trapezoid Trap

Here’s a rather tricky puzzle—perfect for the classroom or a fun activity with your kids (and possibly an excuse to sharpen your own spatial skills).

Print and cut out the five puzzle pieces (see Fig. A), then try to fit them all into the larger shape (Fig. B) without overlapping. Yes, it’s possible… As you may have noticed, all the pieces—including the final shape—are similar right trapezoids. They do, however, vary in scale, just to keep things interesting.

Cut out the 5 puzzle pieces (right trapezoids; fig. A) in order to fit them all into the larger shape (fig. B) without overlapping.

You can download the full template in PDF format here.

The first person to post a correct solution will receive a set of our original postcard designs.

And if you find yourself strangely fascinated by these slanted quadrilaterals, you’re not alone. Even ancient Greek mathematicians toyed with shapes like these to explore proportions and symmetry. Curious about trapezoids (or wondering if they’re secretly out to get you)? Here’s a helpful read: https://en.wikipedia.org/wiki/Trapezoid

Happy puzzling—and remember, if it feels impossible, you’re probably getting close.

(Hint: Some pieces may need to be flipped over, as if seen through a mirror.)

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UMBRELLA ILLUSION

One of my illusions from the late ’90s. Take a look at the colorful umbrellas in Figures A and B—are they the same or different? About 80% of people will say that Umbrella A has jagged, zigzag edges, while Umbrella B has smooth, wavy lines. But here’s the trick—you’ve been fooled by the brightness contrast of the rays inside the umbrellas. In reality, both umbrellas are identical in shape, perfectly congruent.

This illusion shows a phenomenon called curvature blindness, which was rediscovered in 2017 by Japanese psychologist Kohske Takahashi. He created a powerful variant and studied its impact on how we perceive shapes.

© Kohske Takahashi – The wavy lines appear different depending on the background and how the repetitive dark color is applied to them.

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Geometry Meets Illusion

A geometrical optical illusion to explore with your kids!

a. The illusion is created by context.

b. Here, the key factor is perspective.

c. Conclusion: When two objects are the same size, the one that appears farther away will look larger.

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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.

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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!

Read more.

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Walking on Water—No Miracle Needed!

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.

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The Red Wine Color Illusion

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.