The math behind impossible shapes

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If you clicked on this link seemingly confused after seeing this video:

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Design credits: Linus Dalhgren

Then you’re not the only one. Your brain has been tricked by a seemingly impossible figure. 

At this point you may ask, this is a weird, but perfectly and logically constructed triangle. How can this be an impossible figure?

Well, before we dive into it, let’s first clear out what impossible figures mathematically mean?

An impossible figure is a type of optical illusion – consisting of a 2-dimensional (2D) figure that is at first glance perceived as a 3-dimensional (3D) figure. This is done with the clever use of both lighting and your depth perception, thus tricking your brain into thinking there’s no constructional flaw to the impossible object.

The video you just saw, is a product of one such impossible object called the Penrose Triangle, first created by Oscar Reutersvärd, also known as the ‘father of impossible shapes’. The illusion was however later independently discovered and popularized by a British psychiatrist, geneticist and mathematician Lionel Penrose and his son, a British mathematician, physicist and philosopher of science Sir Roger Penrose.

The triangle appears to be a solid figure, made of three cross-section of straight beams that meet pairwise at the right angles, at the vertices that it forms.


If you however, open the Penrose triangle, this is what you see:

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By Tomruen – Own work, CC BY-SA 4.0,

As you can see, it’s architecture is impossible to be recreated in an Euclidean space.

Even though we’ve shown you the broken and actual construction of the triangle, your brain will still not find anything wrong with it’s seemingly impossible construction. 

This proves that there actually exists a split between our conception of something and our perception of something.

There are many variations of impossible objects that have been created time and time again to play tricks on our minds. One such example of an impossible object, can also be found in Christopher Nolan’s widely famous sci-fi movie ‘Inception’. In a scene, Christopher Nolan has shown a live impossible staircase called a Penrose step. 

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Wonderful! Isn’t it? Do you know of any impossible objects? Let us know about it in the comment section below.