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How To Draw An Impossible Triangle Optical Illusion - Impossible Shapes
How To Draw An Impossible Triangle Optical Illusion - Impossible Shapes
Published: 2015/08/28
Channel: My Drawing Tutorials
Amazing 3D Printed Paradox Design - Penrose Triangle
Amazing 3D Printed Paradox Design - Penrose Triangle
Published: 2015/01/17
Channel: 3D Print Headquarters
How To Draw The Impossible Triangle - Optical Illusion
How To Draw The Impossible Triangle - Optical Illusion
Published: 2012/07/06
Channel: Jonathan Harris
Penrose Triangle Illusion Explained with Animation
Penrose Triangle Illusion Explained with Animation
Published: 2015/04/12
Channel: Hind Sight Grafx
Impossible Triangle // How To - Pallet Upcycle Challenge 2016
Impossible Triangle // How To - Pallet Upcycle Challenge 2016
Published: 2016/08/03
Channel: Fabian's Tiny Workshop
Penrose triangle with rolling ball
Penrose triangle with rolling ball
Published: 2014/09/04
Channel: Bryan Wienczkowski
Penrose Triangle WoodPoint
Penrose Triangle WoodPoint
Published: 2017/02/26
Channel: Shaka
How to Draw the Impossible Triangle in Adobe Illustrator
How to Draw the Impossible Triangle in Adobe Illustrator
Published: 2015/09/28
Channel: hikeart
Impossible triangle found in real life! 2 Juli 2013 Ophoven, Belgium
Impossible triangle found in real life! 2 Juli 2013 Ophoven, Belgium
Published: 2013/07/02
Channel: ruudrebel
Create the Penrose (impossible) Triangle in Adobe Illustrator CC!
Create the Penrose (impossible) Triangle in Adobe Illustrator CC!
Published: 2017/01/13
Channel: tutvid
Impossible Escher-style triangle found in real life!
Impossible Escher-style triangle found in real life!
Published: 2009/11/09
Channel: AngryAussie
How to Draw The Impossible Triangle in 3 Different Ways: Narrated
How to Draw The Impossible Triangle in 3 Different Ways: Narrated
Published: 2015/03/28
Channel: Circle Line Art School
Dice Triangle Illusion - Make The Impossible Possible
Dice Triangle Illusion - Make The Impossible Possible
Published: 2014/02/28
Channel: スティーブンの英語塾
Optical Illusion Penrose triangle
Optical Illusion Penrose triangle
Published: 2013/12/27
Channel: Hanif Azwar
How to Draw an Impossible Triangle in a Very Simple Way
How to Draw an Impossible Triangle in a Very Simple Way
Published: 2013/12/06
Channel: Circle Line Art School
How to Draw an Optical Illusion Triangle the Easy Way
How to Draw an Optical Illusion Triangle the Easy Way
Published: 2015/04/06
Channel: Art of Wei
Penrose "Impossible" triangle
Penrose "Impossible" triangle
Published: 2014/02/23
Channel: John
3D Printing of a Penrose Triangle
3D Printing of a Penrose Triangle
Published: 2014/01/12
Channel: VBerstis
The Penrose Triangle - Explained
The Penrose Triangle - Explained
Published: 2013/07/02
Channel: thepuppynews
60 Penrose Triangle Tattoos Tattoos For Men
60 Penrose Triangle Tattoos Tattoos For Men
Published: 2017/03/04
Channel: Next Luxury
Impossible Triangle in Real Life
Impossible Triangle in Real Life
Published: 2016/01/23
Channel: Zach King
How To Draw The Impossible Penrose Triangle for kids - Optical Illusion
How To Draw The Impossible Penrose Triangle for kids - Optical Illusion
Published: 2016/04/17
Channel: PIN KORO
Construire un triangle de Penrose 3d en bois optical illusion
Construire un triangle de Penrose 3d en bois optical illusion
Published: 2016/02/19
Channel: Etp résonne
Impossible Triangle - 3D Illusion Made Using Wood
Impossible Triangle - 3D Illusion Made Using Wood
Published: 2013/08/10
Channel: Shaun Ryan
What is PENROSE TRIANGLE? What does PENROSE TRIANGLE mean? PENROSE TRIANGLE meaning & explanation
What is PENROSE TRIANGLE? What does PENROSE TRIANGLE mean? PENROSE TRIANGLE meaning & explanation
Published: 2017/09/24
Channel: The Audiopedia
Illustrator tutorial: Creating an impossible Penrose triangle | lynda.com
Illustrator tutorial: Creating an impossible Penrose triangle | lynda.com
Published: 2014/07/24
Channel: LinkedIn Learning Solutions
construct an impossible object out of legos a science with bobert video short
construct an impossible object out of legos a science with bobert video short
Published: 2015/12/21
Channel: science with bobert
3D Penrose triangle Photoshop
3D Penrose triangle Photoshop
Published: 2017/09/01
Channel: PicturesqueON
How To Draw a Complex Impossible Triangle
How To Draw a Complex Impossible Triangle
Published: 2012/07/06
Channel: Jonathan Harris
tattoo: Penrose triangle
tattoo: Penrose triangle
Published: 2015/05/20
Channel: pakisu
Penrose Triangle result
Penrose Triangle result
Published: 2009/12/13
Channel: Andris Rozers
The Impossible Triangle - Advanced Photo Manipulation
The Impossible Triangle - Advanced Photo Manipulation
Published: 2017/09/21
Channel: Nemanja Sekulic
Penrose Triangle Expandable Trivet
Penrose Triangle Expandable Trivet
Published: 2015/01/08
Channel: Elyasaf shweka
quickFlow :: Houdini :: Penrose Triangle :: Modeling
quickFlow :: Houdini :: Penrose Triangle :: Modeling
Published: 2017/11/21
Channel: node flow
✔ Minecraft: How to make an Impossible Triangle
✔ Minecraft: How to make an Impossible Triangle
Published: 2015/04/20
Channel: MagmaMusen
Penrose Impossible Triangle revealed
Penrose Impossible Triangle revealed
Published: 2007/12/08
Channel: Shpazz
How To BO3 Emblems | Penrose Triangle (Triangle Illusion!)
How To BO3 Emblems | Penrose Triangle (Triangle Illusion!)
Published: 2016/02/22
Channel: Keokemon
How to Draw The Impossible Triangle in 3D
How to Draw The Impossible Triangle in 3D
Published: 2016/01/03
Channel: Circle Line Art School
Impossible Triangle Optical Illusion - Penrose Triangle - 3D Trick Art
Impossible Triangle Optical Illusion - Penrose Triangle - 3D Trick Art
Published: 2017/09/01
Channel: Epic Squares
How to Draw the Impossible Triangle | Optical Illusion Fun
How to Draw the Impossible Triangle | Optical Illusion Fun
Published: 2017/04/22
Channel: Draw So Cute
How to draw the Penrose triangle
How to draw the Penrose triangle
Published: 2013/06/24
Channel: gilad diamant
A real model of the impossible triangle
A real model of the impossible triangle
Published: 2011/02/16
Channel: trompevenlo
How to make the impossible triangle illusion in Minecraft
How to make the impossible triangle illusion in Minecraft
Published: 2016/06/30
Channel: TINYYT
Fractal Penrose Triangle | Minimal Speed Art Rhinoceros 3D & Illustrator - Vecxtor (Featured Artist)
Fractal Penrose Triangle | Minimal Speed Art Rhinoceros 3D & Illustrator - Vecxtor (Featured Artist)
Published: 2016/10/20
Channel: Pixel & Bracket
DIY Penrose "Impossible" Triangle - How To Build - Wood
DIY Penrose "Impossible" Triangle - How To Build - Wood
Published: 2016/01/27
Channel: tsbrownie
錯視立体 ペンローズの三角形  Penrose Triangle, How to make
錯視立体 ペンローズの三角形 Penrose Triangle, How to make
Published: 2017/10/14
Channel: yattemita325
Penrose Triangle Illusion | Black Ops 2 Emblem Tutorial
Penrose Triangle Illusion | Black Ops 2 Emblem Tutorial
Published: 2012/12/30
Channel: skfemblems
Relativity Penrose triangle
Relativity Penrose triangle
Published: 2013/12/23
Channel: Ainia DaFente
How To Draw An Impossible Triangle Optical Illusion - Impossible Shapes
How To Draw An Impossible Triangle Optical Illusion - Impossible Shapes
Published: 2017/03/21
Channel: Relax & Reset
Escher for Real The Belvedere, Waterfall, Necker Cube, Penrose Triangle 3D Printing from Technion
Escher for Real The Belvedere, Waterfall, Necker Cube, Penrose Triangle 3D Printing from Technion
Published: 2012/08/09
Channel: Technion
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WIKIPEDIA ARTICLE

From Wikipedia, the free encyclopedia
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The Penrose triangle

The Penrose triangle, also known as the Penrose tribar, or the impossible tribar,[1] is a triangular impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The psychiatrist Lionel Penrose and his mathematician son Roger Penrose independently devised and popularized it in the 1950s, describing it as "impossibility in its purest form". It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.

Impossible object[edit]

The tribar appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. The beams may be broken, forming cubes or cuboids.

Impossible triangle sculpture as an optical illusion, East Perth, Western Australia

This combination of properties cannot be realized by any three-dimensional object in ordinary Euclidean space. Such an object can exist in certain Euclidean 3-manifolds.[2] There also exist three-dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the 2-dimensional depiction of the Penrose triangle on this page (such as - for example - the adjacent image depicting a sculpture in Perth, Australia). The term "Penrose triangle" can refer to the 2-dimensional depiction or the impossible object itself.

M.C. Escher's lithograph Waterfall (1961) depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began. The resulting waterfall, forming the short sides of both triangles, drives a water wheel. Escher helpfully points out that in order to keep the wheel turning some water must occasionally be added to compensate for evaporation.

A 3D-printed version of the Reutersvard Triangle illusion
Impossible Triangle sculpture, Gotschuchen, Austria

If a line is traced around the Penrose triangle, a 4-loop Möbius strip is formed.[3].

Although the tribar is named one of the impossible objects, there exist many more that fit into the same category. Other impossible objects include the devil's fork, the dancing elephant, and impossible arch.[4]

Other Penrose polygons[edit]

While it is possible to construct analogies to the Penrose triangle with other shapes and regular polygons to create a Penrose polygon, the visual effect is not as striking, and as the sides increase, the object seems merely to be warped or twisted.

See also[edit]

References[edit]

  1. ^ Pappas, T. "The Impossible Tribar." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 13, 1989.
  2. ^ Francis, George (1988). A topological picturebook. Springer. ISBN 0-387-96426-6.  In the chapter on the Penrose tribar, Francis attributes this observation to John Stillwell.
  3. ^ Gardner, Martin (1978). Mathematical Games, August 1978 A Möbius band has a finite thickness, and so it is actually a twisted prism. SCIENTIFIC AMERICAN, A DIVISION OF NATURE AMERICA, INC. 
  4. ^ Adamovic, Jan. "BrainDen.com - Impossible Objects". BrainDen.com. Retrieved 2016-02-09. 

External links[edit]

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