Penrosetriangel

Penrosetriangel
«Impossible Triangle sculpture», East Perth, Australia. Konstruksjonen er ikke festet sammen, og bildet er tatt fra en av de to vinklene som gir inntrykk av at koblingen er der. Flere bilder fra andre vinkler.

Penrosetriangelet er et umulig objekt. Den svenske kunstneren Oscar Reutersvärd laget bildet av «konstruksjonen» i 1934. Matematikeren Roger Penrose kom til samme idé omkring 1950-årene og beskrev den som «umulighet i sin reneste form». Kunstneren Maurits Cornelis Escher var inne på samme spor og var inspirasjonen til Penroses arbeid[1].

Triangelet gir skinn av å være en solid tredimensjonal figur, laget av tre like lange bjelker som møtes parvis i rette vinkler mot hverandre i hjørnene av en noe skjev sammensetning. Dette lar seg gjøre på papiret, slik illustrasjonen viser, men kan ikke virkeliggjøres i tre dimensjoner.

M.C. Eschers litografi: Vannfall forestiller et vannløp som flyter i sikk-sakk langs langsidene av to forlengede Penrosetriangler, og ender opp to etasjer høyere enn startpunktet. Vannfallene som utgjør kortsidene av trianglene driver vannhjul. Eschers hjelpsomme kommentar var at hvis man ville ha hjulene til å fortsette å snurre, trengtes påfyll av og til for å kompensere for fordampningen.

Hvis man trekker en midtlinje langs sidene i dette triangelet, vil man til slutt komme tilbake til utgangspunktet. Figuren er en tre-vridd möbiusstripe.

En tilsvarende umulig figur er Penrosetrappa.

Andre Penrosepolygoner

Den visuelle virkningen avtar med å innføre flere hjørner.

Referanser

  1. ^ https://www.bbc.co.uk/sounds/play/live:bbc_radio_fourfm

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