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The Penrose Triangle

Have you ever seen the Penrose Triangle? The logo for Project Enigma is based on this famous 2-D optical illusion that was first created by Swedish artist Oscar Reutersvärd and later popularised by Roger Penrose, whose name it now bears.

(One version of the Penrose Triangle. Taken from Pixabay)


(Another version of the Penrose Triangle which inspired our logo. Taken from The Illusions Index)


The Impossible Triangle

As you may have noticed, the Penrose Triangle cannot exist in reality. At first glance, the three sides of the triangle seem to fit neatly together, but a closer inspection reveals the structural inconsistencies of this object. Starting from the top of the triangle, the viewer perceives the left side of the triangle to be further away than the right side; yet, both sides are connected along the same plane at the base of the triangle. While this visual trick can be achieved on paper, it is impossible to create a real-life Penrose Triangle because it violates the rules of Euclidean geometry.


A creative way around this problem is to use forced perspective to achieve the same result. The two sides of a real-life Penrose triangle are not actually linked together at the vertex, but from a certain viewpoint they do look attached to each other, creating the same illusion. Check out this impossible triangle sculpture in Perth, designed by Architect Ahmad Abas and Artist Brian McKay:

(Taken from Wikipedia)


The Penrose Triangle is just one example of an impossible object. Other famous impossible objects that you may have come across include the impossible trident and the impossible cube. These also use visual tricks and play on perspective to project a 3-D image of an object which defies human logic.


The Penrose triangle has been incorporated into other famous illusions too, such as the Penrose Stairs (never-ending stairs) and Escher’s Waterfall (perpetual motion machine). The concept of impossible shapes has even been used in phone games; Monument Valley (available on both IOS and Android) is a visually stunning game where the player tries to navigate the character Ida through a series of puzzles/mazes, which are designed based on impossible objects.

(Shots from the game Monument Valley taken from engadget)


So, why did we choose this particular shape as our logo for Project Enigma?


Project Enigma’s own twist on the Penrose Triangle…

The Penrose Triangle is a fitting logo for Project Enigma. On the one hand, it is mystifying, an impossible object that projects a strange illusion. Similarly, many science toys in our collection are designed to move and function in seemingly unnatural ways (e.g., Euler’s disk or Tippe tops). Yet, the “illusion” they portray can be explained by making reference to science, and the forces that are at work (gravitational, centrifugal etc.) on them.


At the same time, the Penrose Triangle is an intriguing drawing that gets us to think. It sparks our curiosity and prompts us to look at it closer. In the same way, the mechanical puzzles we offer are designed to attract and draw one’s attention to the fine details within each of them. Many times, the solution to these puzzles requires a keen eye to notice a particular recurring pattern or a tiny detail e.g., one piece of the puzzle that can be manipulated in a different way or orientation.


The colour of our Penrose Triangle logo, orange, has also been chosen intentionally. “Orange” is the colour most commonly associated with happiness, creativity, vibrancy and fun. These are emotions and qualities that we seek to promote through our products. We hope that our customers will be excited and have a good time with their friends and family as they play with the different toys and puzzles available. Our “enigmatic” collection is sure to provide hours of joy and mental stimulation.


In addition, each side of the triangle represents an aim of Project Enigma. We have three main aims: 1) to raise awareness about, 2) increase accessibility to, and 3) improve affordability of mechanical puzzles and other enigmatic objects. Our organisations’ guiding philosophy also follows a three-part formula: we seek to act in the interest of people, and the planet, and generate sustainable profits. The harmonious confluence of these three principles undergirds all of our work. Furthermore, similar to how the triangle is the most stable and rigid shape used in structures, we hope to build a strong foundation for our company based on these tripart goals and philosophy.


Yet another reason for choosing the Penrose Triangle (an impossible object) as our logo is that we have several impossible puzzles in our collection! These are puzzles that on first glance appear to have no solution, but can be solved with some ingenuity (and often dexterity). Sometimes, the goal is simply to explain how these objects are made. Examples include the Impossible Braid (challenge and solution), Impossible Dovetails (different versions here and here), and Impossible Bottles.


Finally, you may have noticed that our Penrose Triangle logo is actually incomplete. One of its lines (the base of the triangle) is broken. This “gap” was included on purpose. It serves as a simple reminder for us that our work remains incomplete. We still have much to do on our mission to improve lives through play; it is an ongoing endeavour.


As a young organisation, we acknowledge the long journey ahead of us, but strive towards our goals nonetheless. We want to continue making a positive impact on the lives of others, and the broken Penrose Triangle is a powerful image that reflects this ongoing pursuit of ours.


If reading this article has piqued your curiosity about our work, check out our Sparkbox Plans or contact us here for any other queries you may have. :) We have several other exciting plans in store for the future, so stay tuned!


References

Jennifer Bourn. “Color Meaning: Meaning of the Color Orange.” Bourn Creative. https://www.bourncreative.com/meaning-of-the-color-orange/#:~:text=Orange%20is%20associated%20with%20meanings,color%20of%20joy%20and%20creativity.


Areeba Merriam. “What Makes an Impossible Figure Impossible?” Cantor’s Paradise.

https://www.cantorsparadise.com/what-makes-an-impossible-figure-impossible-98bf40effdc0


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