12/6/2023 0 Comments Impossible shapes aThis album is their pinnacle song mound that could have been issued by Zapple, if times had been different. With this release the band has recorded songs which were flushed out over many live performances over many tours all across the globe. Vertical or Horizontal Slices? Riemann and Lebesgue Integration.The Impossible Shapes have been merrily musickmaking - mostly under the radar - for a decade now.Dynamic Similarity and the Reynolds Number July 20, 2023.Margules’ Tendency Equation and Richardson’s Forecast July 27, 2023.Maths in the Time of the Pharaohs August 3, 2023.Music and Maths from Bach to Bacherach August 17, 2023. ![]() Retroreflectors: Right Angles Save Lives August 24, 2023.Sixth Irish History of Mathematics (IHoM) Conference August 31, 2023.Hamilton’s Semaphore Code and Signalling System September 7, 2023.A Memorable Memo: Responding to Over-assiduous Administrators September 14, 2023.Maths in Action at the Rugby World Cup September 21, 2023.A Remarkable Sequence in OEIS September 28, 2023.Digital Signatures using Edwards Curves October 5, 2023.Elusive Transcendentals October 12, 2023.Earth’s Digital Twins can help us to avert Disaster October 19, 2023.The Axiom of Choice: Shoes & Socks and Non-constructive Proofs October 26, 2023.Yin and Yang - and East and West November 2, 2023.The Logistic Map: a Simple Model with Rich Dynamics November 9, 2023.The citation stated that Penrose showed that “black hole formation is a robust prediction of the general theory of relativity” He shares the prize with two astrophysicists who discovering a black hole at the centre of the Milky Way. The prize was awarded to Penrose for showing how black holes can form. Roger Penrose has been awarded half of the 2020 Nobel Prize in Physics for work first presented in his 1965 paper “Gravitational Collapse and Space-Time Singularities”. This also inspired Escher to produce a lithograph, Ascending and Descending, which depicts a never-ending staircase on the roof of a large building. It appears to de scend clockwise and ascent anticlockwise, and yet we arrive back at the same spot after one cycle, whichever way we go. It incorporates the structure of the tribar in an essential way.Īnother illusion devised by Penrose is the curious cyclic staircase shown here. ![]() Escher’s well-known masterpiece Waterfall shows water flowing over a mill-wheel and returning in a zig-zag channel to the top again. ![]() Penrose sent a copy of an article on the shape to Escher, who was strongly influenced by it. Penrose has described it as “impossibility in its purest form”. Together with his father Lionel, Penrose popularised the shape, and it has since appeared in countless books on art, psychology and mathematics, and elsewhere. In fact, the shape had already been discovered in 1934 by a Swedish artist Oscar Reutersvärd, but had apparently attracted little notice at the time. Seen from the correct angle, it appears to be a Penrose triangle. There is an “Impossible Triangle sculpture in Perth, Western Australia (see figure at the top of this post). However, a construction with three straight square bars can be made that, when viewed from a certain angle, appears to be a tribar. It cannot be realized as a closed loop in our 3D space. The tribar appears to be a solid triangular object made from three straight sections, each with square cross-section, meeting at right angles to each other.
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