Geometrical illusions are examples of how our mind tries to find orderly representation out of ambiguous, disordered 2D images. The images transmitted to our brain from our retina are an imperfect representation of reality; our visual system is capable of processing the information received from our eyes to extract meaningful perceptions. However, this can sometimes go wrong, leading to faulty perceptions.

Illusion of Position: Poggendorff Illusion

The Poggendorff illusion is an image where thin diagonal lines are positioned at an angle behind wider stripes. The blue line on the right appears to line up with the black line on the left, however in actuality, the black and red lines match up.

File:Poggendorff illusion.svg

Illusion of Length: Müller-Lyer illusion

The Muller-Lyer illusion is a well-known optical illusion in which two lines of the same length appear to be of different lengths.

Source: Wikipedia

Illusions of Orientation

Zöllner illusion

In this illusion, the black lines do not seem to be parallel, but in reality they are.


Source: Wikipedia


Café Wall illusion

This is an optical illusion in which parallel straight dividing lines, between staggered rows with alternating black and white ‘bricks’, appear to be sloped.

Source: Wikipedia

Illusion of Size: Delboeuf Illusion

Two circles of identical size are placed near to each other and one is surrounded by an annulus (ring-shaped object). The surrounded circle appears larger than the non-surrounded circle if the annulus is close, while appearing smaller than the non-surrounded circle if the annulus is distant.


Illusion of the Straightness of Lines: Hering Illusion

When two straight and parallel lines are placed in front of radial background, the lines appear as if they were bowed outwards.

Source: Wikipedia

Illusions of Vertical/Horizontal Anisotropy

The vertical–horizontal illusion demonstrates the tendency for observers to overestimate the length of a vertical line relative to a horizontal line of the same length.

Source: Wikipedia

Impossible Objects

Impossible objects consist of 2D figures which are subconsciously interpreted by our visual system as representing a projection of a 3D object.

Penrose Triangle

Although it was first created by the Swedish artist Oscar Reutersvärd in 1934, Lionel and Roger Penrose independently devised and popularised the Penrose triangle in the 1950s, describing it as “impossibility in its purest form”.


Penrose Staircase

The Penrose staircase is a variation on the Penrose triangle, and is a two-dimensional depiction of a staircase that seems to form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions.

Source: Wikipedia

Impossible Fork/Blivet

The impossible fork appears to have three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end.

Source: Wikipedia

Sources: 1 | 2

Hope you enjoyed this round up of some mathematical optical illusions! M x



11 thoughts on “Illusions”

  1. Pingback: Illusions
    1. Yes! Reutersvärd was one of the first artists to deliberately draw impossible objects, although many other artists have followed in his footsteps.
      Thank you! Really glad you enjoy them!


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