Aesthetic Exploration: Impossible Triangle

The impossible triangle, or Penrose Triangle is a shape that cannot be made by any 3 dimensional object in ordinary Euclidean Space. This style of artwork was first started by Swedish artist Oscar Reutersvard in 1934 and was later discovered independently by a psychiatrist Lionel Penrose and mathematician son in the 1950’s who famously described it as “Impossibility in its purest from”. Artist M. C. Escher brought this form of art to the mainstream as it was a prominent feature of his artwork.

[1] https://ih1.redbubble.net/image.120549726.9405/flat,800×800,075,f.u1.jpg

This is a simple computer generated image that shows what exactly the Penrose Triangle is and why its geometry is impossible.

[2] farm5.staticflickr.com/4006/4589604335_e41af5926e_z.jpg

This image is someone’s attempt at a paper Penrose Triangle. You can see the rough edge on the lower right corner showcasing the artist using a forced perspective when photographing his piece. This makes it look like he achieved the impossible shape.

[3] mediad.publicbroadcasting.net/p/nhpr/files/201409/5-Escher-Waterfall_0

This is one of my personal all time favorite pieces of art. Artist M. C. Escher uses the idea of the Penrose Triangle and takes it further. The waterfall can’t possible turn that waterwheel as the water returns to the aqueduct by defying gravity and traveling back up to the top of this structure only to be dropped on the waterwheel again. This creates another impossible machine, one that creates perpetual motion.

Other Sources:

https://en.wikipedia.org/wiki/Impossible_object

http://www.michaelbach.de/ot/cog_imposs1/

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3 Comments. Leave new

  • Heckuva good job. I sure appaicerte it.

    Reply
  • Avery Anderson
    Matthew Clark
    January 29, 2017 7:45 pm

    The Penrose triangle has fascinated me ever since I first saw it. At a glance, you notice a simple triangle shape but upon further inspection, you notice that the object cannot physically exist in our normal vantage point. As you try to follow the edges of the triangle around, the sides make 90 degree angles with each other, which defies the geometry of a triangle!

    Reply
  • I really like your topic, and a big fan of M. C. Escher. I wonder how the process of planning these drawings might be? The impossible triangle has a mystical or spiritual aura about it. Art using forced perspective and impossible geometries almost always convey a feeling of deeper consciousness to me. It draws in the viewer to indulge longer and look out for the smaller details in the art piece. Great post!

    Reply

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