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Penrose Triangle

PenroseTriangle

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published by Penrose and Penrose (1958). Penrose triangles appear prominently in the works of Escher, who not only inspired creation of this object (Escher 1954, Penrose and Penrose 1958), but also subsequently publicized it.

The Penrose triangle can be extended to n-gonal barred objects (Cerf, Elber), including the so-called tribox.

Penrose triangle stamp

The figure was drawn earlier by artist Oscar Reutersvärd in 1934 during a "long lecture." For this, he was honored with a stamp by the government of Sweden in 1982 (Miller).

The Penrose triangle appears on the cover of Raghavachary (2004).

Henderson (2006) offers an impossible triangle net.

See also

Impossible Figure, Impossible Joinery, Tribox

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References

Bool, F. H.; Kist, J. R.; Locher, J. L.; and Wierda, F. M. C. Escher: His Life and Complete Graphic Work. New York: Abrams, p. 147, 1982.Cerf, C. "A Family of Impossible Figures Studied by Knot Theory." http://www.mi.sanu.ac.yu/vismath/cerf/.Cowan, T. M. "Turning the Penrose Triangle Inside Out." J. Math. Psych. 26, 252-262, 1982.Cowan, T. M. "The Theory of Braids and the Analysis of Impossible Figures." J. Math. Psych. 11, 190-212, 1974.Draper, S. W. "The Penrose Triangle and a Family of Related Figures." Perception 7, 283-296, 1978.Elber, G. "Escher for Real." http://www.cs.technion.ac.il/~gershon/EscherForReal/.Ernst, B. "The Tri-Bar." Ch. 1 in Adventures with Impossible Figures. Stradbroke, England: Tarquin, pp. 9-23, 1987.Escher, M. C. Catalogus 118. Amsterdam, Netherlands: Stedelijk Museum, 1954.Henderson, S. "Make Your Own Impossible Triangle." http://www.coolopticalillusions.com/build-an-impossible-triangle.htm.Knuth, D. E. §7.2.2.3 in The Art of Computer Programming, Vol. 4. Pre-Fascicle 7A, pp. 15-16, Dec. 5, 2024.Miller, J. "Other Mathematics Stamps: Impossible Figures of Oscar Reutersvärd." http://jeff560.tripod.com/impossible1.jpg.Pappas, T. "The Impossible Tribar." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 13, 1989.Penrose, L. S. and Penrose, R. "Impossible Objects: A Special Type of Visual Illusion." Brit. J. Psychology 49, 31-33, 1958.Raghavachary, S. Rendering for Beginners: Image Synthesis using RenderMan. Focal Press, 2004.Robinson, J. O. The Psychology of Visual Illusion. New York: Dover, pp. 176-177 and 181, 1998.Seckel, A. The Art of Optical Illusions. Carlton Books, p. 32, 2002.

Referenced on Wolfram|Alpha

Penrose Triangle

Cite this as:

Weisstein, Eric W. "Penrose Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PenroseTriangle.html

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