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While the Penroses credited Escher in their article, Escher noted in a letter to his son in January 1960 that he was: Escher was captivated by the endless stairs and subsequently wrote a letter to the Penroses in April 1960:

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That second proof was fueled by another stunning finding: after discovering “the hat”, Smith landed on another shape that did the same job and looks a bit like a turtle. Myers found that the turtle and hat were geometrically linked and led to a whole family of einstein shapes, the Times reported. Penrose Stairs. Benedikt Taschen. 1992. ISBN 9783822896372. Archived from the original on 23 November 2022 . Retrieved 9 October 2020. John Penrose MP has today (16 February) published proposals to update the UK’s competition and consumer regime. It’s unclear what the discovery could lead to outside the world of mathematics, but “there are lots of great real-world applications in art, design, architecture”, says Kaplan. “The race is on to be the first person to take a photo of their bathroom floor tiled in hats.” Smith says it could help in studying structures known as quasicrystals. And outside interest in the finding has ballooned.Hallyn, Fernand (2000). Metaphor and Analogy in the Sciences. Springer. ISBN 978-0-7923-6560-0 . Retrieved March 16, 2011.

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Mr Penrose recommends further work to strengthen and speed up enforcement of consumer and competition law. Such a shape would be known as an aperiodic monotile, or “einstein” shape, meaning, in roughly translated German, “one shape” (and conveniently echoing the name of a certain theoretical physicist).

working on the design of a new picture, which featured a flight of stairs which only ever ascended or descended, depending on how you saw it. [The stairs] form a closed, circular construction, rather like a snake biting its own tail. And yet they can be drawn in correct perspective: each step higher (or lower) than the previous one. [...] I discovered the principle in an article which was sent to me, and in which I myself was named as the maker of various 'impossible objects'. But I was not familiar with the continuous steps of which the author had included a clear, if perfunctory, sketch, although I was employing some of his other examples. [10] A few months ago, a friend of mine sent me a photocopy of your article... Your figures 3 and 4, the 'continuous flight of steps', were entirely new to me, and I was so taken by the idea that they recently inspired me to produce a new picture, which I would like to send to you as a token of my esteem. Should you have published other articles on impossible objects or related topics, or should you know of any such articles, I would be most grateful if you could send me further details. [10] In his report, Mr Penrose outlines options to promote competition in the UK and to improve consumer confidence.This includes proposals to protect consumers from new kinds of rip-offs, and to ensure that they can expect fair treatment, particularly in online transactions.

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a b … n ε a b … n {\displaystyle \varepsilon _{ab\ldots n}\,\varepsilon In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting upwards and downwards, corresponding to abstract upper and lower indices of tensors respectively. Connecting lines between two shapes corresponds to contraction of indices. One advantage of this notation is that one does not have to invent new letters for new indices. This notation is also explicitly basis-independent. [3] Matrices [ edit ] Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler) (1988) Harshbarger, Eric (2010-08-19). "The Never-Ending Stories: Inception's Penrose Staircase". Wired. ISSN 1059-1028 . Retrieved 2020-06-05. Graphical notation for multilinear algebra calculations Penrose graphical notation (tensor diagram notation) of a matrix product state of five particles