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$$e = \sum_{n=0}^\infty \frac{1}{n!}$$
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penrose tribar, the impossible infinite triangle

Sunday, 24 June 2018 07:56

## penrose tribar, the impossible triangle

celebrated as a paradox or a unique contradiction, a mystery that can’t be solved...
a triangle that looks like a real, solid three-dimensional object, but isn't.
The impossible triangle, infinite triangle, penrose tribar, impossible tribar, is a triangular impossible object.
a continuous loop, an ambiguous figure, a visual paradox;
a strange loop with tangled hierarchies.
impossibility in its purest form

looks like a simple object. 2d depiction of a 3d triangle built from square beams. The eyes travel from face to face of the object, everything looks great, no problem. As the viewer traverses the continuous impossible object their perspective flips back and forth between equally possible perspectives in an unconscious and automatic way.

implicit in this strange loop is the concept of infinity. a loop representing an endless process in a finite way. -a conflict between the finite and the infinite.

helps give a sense that perceptions are limited and subjective from those of another person viewing the same thing.

A "penrose" polygon refers to the 2-dimensional depiction of the impossible object itself.
Penrose triangle - Wikipedia
Roger Penrose was the inventor of the tribar.
it's also an interesting look at Escher.
video with the Roger Penrose talking about the discovery of the tribar (spanish).
Escher's works like ascending decending, waterfall, and other tilings are influenced by the Penrose father and son's work.
non-isohedral tilings, tiles only one shape but they have different roles to play in different parts of the pattern. Roger sent Escher a wooden non-isohedral block puzzle to Escher; and Escher's solution was in Escher's final print "Ghosts" which he made just before he died. Roger says in the video "Unfortunately, Escher died before the non-periodic tilings that came somewhat later."

Tessellations - M.C. Escher Ghosts - Escher's last tessellation "Ghosts" was a solution to a puzzle sent to him by Roger Penrose, the mathematician. Escher solved it and, true to form, changed the angular wood blocks into rounded 'ghosts'.

if a line is traced around the Penrose triangle, a 4-loop Möbius strip is formed....

and ya, that's my leg and first tattoo. and ya, I'm white and nerdy. Thank you Samuel Hyndman

60 Penrose Triangle Tattoo Designs For Men - Impossible Tribar Ideas -
Triangle Tattoo Meaning | herinterest.com/
Impossibility on Behance
Making a Penrose Triangle on Behance - make a penrose perspective paper and tape model.
If you're interested in optical illusions, you might also checkout Optical tricks and illusions - Dave Horner's Website.

## should maybe be on another penrose page but...

Tilings
Penrose tiling - Wikipedia
Aperiodic tiling - Wikipedia
Penrose Tiles -- from Wolfram MathWorld
Impossible Cookware and Other Triumphs of the Penrose Tile - Issue 13: Symmetry - Nautilus
Anisohedral tiling - Wikipedia - In geometry, a shape is said to be anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that shape there are two tiles that are not equivalent under any symmetry of the tiling. A tiling by an anisohedral tile is referred to as an anisohedral tiling.
Isohedral figure - Wikipedia -isohedral or face-transitive when all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.
Penrose diagram - Wikipedia - is a two-dimensional diagram capturing the causal relations between different points in spacetime. It is an extension of a Minkowski diagram where the vertical dimension represents time, and the horizontal dimension represents space, and slanted lines at an angle of 45° correspond to light rays.
Orchestrated objective reduction (Penrose–Lucas argument) - Wikipedia - The Penrose–Lucas argument states that, because humans are capable of knowing the truth of Gödel-unprovable statements, human thought is necessarily non-computable.

AMS :: Feature Column :: The Topology of Impossible Spaces
The Penrose Tribar(pdf)
Drawing A Tribar Figure by Hand(pdf)
AMS :: Feature Column :: The Topology of Impossible Spaces - this page includes amazing pictures and walks you through the math behind perspective and how to know if an object is impossible in mathematical terms. 1-dimensional cohomology
Impossible Triangle - this page right here has wonderful english to walk you through what's going on in a tribar, i highly recommend it. "The beams of the triangle simultaneously appear to recede and come toward you. Yet, somehow, they meet in an impossible configuration!" "it is possible to construct a physical model of the impossible triangle that looks impossible from only one angle" "It would lead to biological disaster if you were blind to the unusual, inconsistent, or paradoxical." "When you examine a drawing of an impossible triangle, you first build up a global image by examing the local parts." "When you examine a drawing of an impossible triangle, you first build up a global image by examing the local parts."
Impossible Triangle - The Illusions Index - another good page with wonderful english description of impossible triangle. It also includes a four sided impossible figure.

Last Updated on Thursday, 09 August 2018 15:06

 No Really. roll Riiight. Sunday, 21 September 2014 22:17 who||what needs to be the focal point now? ℝ ℚ self-manage Δ participation Α↔ℍ↔Ω Tweets by @MrHorner2U u'll find changed perception when that occurs && fall deeper into key. Tweets by @MrHornerToYou what's a matter?, I'm not sure myself; happy to talk with u about it. good luck with that; whatever ℎ might happen to =. best to speak in code && deal in the truths as u & I see && define them.(the details always fall in place don't they; magically!) think for urself. more toward. move away. R u steady now? Under control? I know well. mutual attractiveness; mitigating circumstances; points of (de|re)flexion: freedom in the 21st century. irrationality enslaved by selfish genes. u and other. do we reach the other side? conscious purpose in continuous pattern. !automatic where&&when internal meets external. nobody wants to be played. find the truth. control the machine. patience. play. since neither dare lower it's head to other; no 1 wins. here; missing finger, phase-wrapped nose. sometimes both. classical approach. smooth out. control your instrument. find|phone|follow a friend. ICE-COLD. uncover intangible tones in the neglected garden. R u being authentic you && Am I being authentic me? pin point minor 3rd. arrive at same point u start. tonality of self. Don't try, play the notes as they come. use cycle; make statement, apply and progress. divide && conquer. resolve and add it up. do us all a favor. 10 types of relationships. those that do; those that do not. YOLO; illustrate the sound of ur tonality && rythmn of love. JFDI fix what u see as broken; walk away from that which can't be fixed in the time && energy we have. change your life, change others lives. Or; maybe, hopefully the field technician||someone will realize && fix the (phase-wrapped nose||morphine drip) 4 u. (here's hoping; steady as she goes. here we go again. what's ur constant problem?) snap back to reality. communicate the constants which are apparent in your life. share && save us all the time&|energy of doing it without u. r ya here for a reason? I'm not sure myself. Α↔ℍ↔Ω is quite an expanse; - get in where u fit in. lexeme&&lemma, unidirectionality hypothesis, cline of instantiation. find what you like?. what's your truth? stand in solidarity of|with something. splash around; go ahead. where's the genie in aladdin's lamp? Deus Ex Machina. i'll wait. find && study the bounds of the problem. You've got time. mixed up in the wash; hang me out to dry. Are you steady now? like the whites the whites of your eyes. can you hear the bells? joyful. && triumphant. Dumb. Dumb Dumb. Snost & lost. how many miles from 46825 ↔ 518031? you tell me Last Updated on Thursday, 15 January 2015 22:04

 many sides to every story. Sunday, 24 August 2014 23:27 Tweets by @davehorner Tweets by @DaveDaWizard

 random vs random Thursday, 27 March 2014 19:58 to infinity without comprehension. moves in current game:0 black:0 white:0 draws:0 [stop] [slower] [faster] last game: min moves: max moves:0 total games:0 total moves:0