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The Penrose Triangle is a classic example of an impossible shape, defying the laws of three-dimensional space. Moment Open/Getty ImagesThe term 'impossible shape' seems contradictory. If a shape can be drawn, it must exist, right? While these shapes can indeed be illustrated on paper, they cannot be physically constructed in three-dimensional space.
Impossible shapes are fascinating optical illusions. When viewing a two-dimensional drawing, our brain interprets it as a three-dimensional object, attempting to make sense of the shapes. However, impossible shapes contain spatial inconsistencies that create the illusion of depth, which cannot exist in reality. Our brain struggles to process these 'incorrect' drawings, trying to reconcile them into something tangible and comprehensible, but ultimately fails [sources: BrainDen, New World Encyclopedia].
Still puzzled? You're not the only one. Let's explore some impossible shapes and learn how to draw one. This will give you a clearer understanding of their nature and functionality.
The Most Famous Impossible Shapes
Among the most renowned impossible shapes are the Penrose triangle, Penrose stairway, Freemish crate, and the impossible trident [source: The Worlds of David Darling]. The Penrose triangle, also known as the tribar, is named after physicist Roger Penrose. Although Penrose didn't invent it—Swedish artist Oscar Reutersvärd did in 1934 using a set of cubes—it gained popularity after Penrose featured it in a 1958 article in the British Journal of Psychology, co-authored with his father, Lionel. In 1982, the Penrose triangle was commemorated on a Swedish postage stamp to honor Reutersvärd [source: New World Encyclopedia].
The Penrose stairway consists of a staircase that turns four times at 90-degree angles. At first glance, it appears to form a square, resembling a conventional set of stairs. However, upon closer inspection, you realize that no matter how many times you ascend or descend, you never actually move higher or lower—or anywhere at all! The Penrose duo also illustrated this stairway in their 1958 paper [sources: Harshbarger, BrainDen].
The Freemish crate debuted in the 1958 lithograph "Belvedere" by Dutch artist M.C. Escher. In the artwork, a man sits on a bench holding the crate, with the bench positioned at the base of a massive structure. This crate is also referred to as Escher's cube or Hyzer's illusion [source: Wolfram MathWorld].
The impossible trident goes by many names: ambiguous trident, blivet, devil's pitchfork, hole location gauge, Schuster's Conundrum, three-pronged poiuyt, three-legged widget, and two-pronged trident [sources: BrainDen, New World Encyclopedia]. This object seems to have three cylindrical prongs from one perspective, but two rectangular prongs from another. Its origin remains a mystery, though it appeared in various publications (aviation, engineering, and science fiction) in May and June 1964, as well as in a 1964 article by D.H. Schuster in the American Journal of Psychology, earning it the name 'Schuster's Conundrum' [source: New World Encyclopedia].
While the Penrose triangle is simple to draw, creating an impossible shape from scratch is no small feat. Roger and Lionel Penrose, who brought fame to the Penrose triangle and Penrose staircase, were brilliant minds. Lionel, a medical geneticist, and Roger, a physicist and mathematics professor at Oxford University, earned the prestigious Wolf Prize for Physics in 1988, sharing it with Stephen Hawking [source: World of Escher].
How Do I Draw Impossible Shapes?
Let's face it—you're eager to try drawing an impossible shape. It's no wonder! Think back to the joy of learning to draw a cube as a child. You'd sketch one square, overlap it with another, and connect them with diagonal lines. Suddenly, a cube appeared!
While some impossible shapes are complex and challenging to draw, there's a simple method to create one using common shapes like squares, triangles, stars, and pentagons. Let's start with a triangle [source: Snapguide]:
- Start by sketching a triangle.
- Extend a line outward from each corner.
- From each extended line, draw another line that slightly overlaps the corners.
- Almost there! At the end of each line, create a short 45-degree angle that aligns with the opposite side.
- Finally, connect the lines, and voilà—you've created an impossible shape!
A detailed, step-by-step tutorial on drawing impossible shapes.
© 2015 Mytour, a division of Infospace LLCFollow these fundamental steps to craft impossible shapes from various forms. It’s simpler than you might think.
How Impossible Shapes Inspire Art
This diorama places Peeps rabbits within the intricate black-and-white geometry of M.C. Escher's iconic piece "Relativity." Escher remains the unparalleled master of impossible shapes.
The Washington Post/Getty ImagesImpossible objects captivate the imagination. You can spend hours examining their lines, attempting to uncover the 'trick' that makes them appear both real and unreal simultaneously. It's no surprise they often inspire artists to reinterpret them. M.C. Escher stands as the most renowned artist in the realm of impossible constructions.
Escher, a Dutch graphic artist, created nearly 450 lithographs, woodcuts, and wood engravings, along with over 2,000 drawings and sketches. He was deeply intrigued by impossible objects and played a key role in popularizing the Penrose triangle, which he featured in many works. One notable example is "Waterfall, a lithograph depicting a waterway flowing uphill and culminating in a waterfall. The waterfall forms the short sides of two Penrose triangles, though this detail may go unnoticed unless specifically sought [sources: New World Encyclopedia, The Worlds of David Darling, M.C. Escher].
Escher was also inspired by Lionel and Roger Penrose's Penrose stairway. His famous print "Ascending and Descending" clearly reflects the influence of this impossible staircase [source: The Worlds of David Darling].
Artists worldwide have been captivated by impossible objects. For instance, a polished aluminum sculpture of the Penrose triangle, crafted by Brian McKay and Ahmad Abas in 1997, stands in Claisebrook Square, East Perth, Australia [source: Alexeev]. Additionally, the Penrose triangle was originally conceived by Swedish artist Oscar Reutersvärd.
