{"id":277,"date":"2009-01-09T01:00:37","date_gmt":"2009-01-09T01:00:37","guid":{"rendered":"https:\/\/morris.cymru\/?p=277"},"modified":"2023-07-09T21:51:19","modified_gmt":"2023-07-09T20:51:19","slug":"penroses-patent-and-the-battle-of-the-tissue-tiles-contains-mathematics","status":"publish","type":"post","link":"https:\/\/morris.cymru\/en\/2009\/01\/penroses-patent-and-the-battle-of-the-tissue-tiles-contains-mathematics\/","title":{"rendered":"Penrose’s Patent and the Battle of the Tissue Tiles (Contains Mathematics)"},"content":{"rendered":"

\"Penrose<\/a><\/p>\n

This drama has got it all – art, law, maths, a genius professor\/knight, a multi-national company, a courtroom…<\/p>\n

I was reading about Roger Penrose<\/a> and I realised that today is the 30th anniversary of his success in applying for a patent on Penrose tiling<\/a>. So this isn’t exactly news, but the anniversary is my excuse to post up some cool links.<\/p>\n

Penrose tiling was discovered in 1974. You can pick up the idea behind it pretty quickly.<\/p>\n

We’re familiar with bathroom tiles and similar types of designs that have translational symmetry. In other words, they repeat after a while. Penrose tilings don’t repeat. They are non-periodic. But they also have five-fold rotational-symmetry.<\/p>\n

This combination of properties had never been seen before. People assumed it was impossible until Penrose came along and drew one. Awesome scenes, no?<\/p>\n

If you want to investigate this for yourself, you can start with some pretty pictures<\/a> and then delve into the actual maths<\/a>.<\/p>\n

Penrose successfully got the patent<\/a> through on 9th January 1979. And that’s where it gets contentious as there are people who would take issue with this. It was undeniably an innovative step and in this instance a patent can incentivise further discovery and get some pay-off for a mathematicians’s hard work. But is it right to award patents to mathematicians who discover stuff that’s lying around in the Universe? I’m not at all sure it is right, but that’s what happened. Happy birthday patent!<\/p>\n

Much later on, in 1997<\/a>, Mrs Penrose came home with some Kleenex toilet roll from the supermarket. Her husband, the prof, was shocked to discover that the pattern on the roll of tissue was based on his tiling. There’s a good summary of the beginning of the story here<\/a>. It couldn’t have been an exact copy because the original is non-repeating. Apparently the design prevents bunching of the roll because it’s non-periodic. Penrose sued the company and later won<\/a>.<\/p>\n

I think I’m right in saying the patent will have expired by now, if you want to make anything with the design.<\/p>\n

I first heard this story in a mathematics lecture in 2002, my final year at Cardiff University. It was during a module called Non-Commutative Geometry. I won’t try and pretend otherwise – in truth that module was an absolute beast, every bit as difficult as it sounds.<\/p>\n

I’m not totally sure why I find myself continually revisiting school and university in this blog. Maybe I have unfinished mental tidying to do.<\/p>\n

Anyway, my lecturer at the time showed us Penrose tiling and related the Kleenex story. In a flourish (and this was a flourish by maths undergrad standards, yours may differ), he ended the story by saying “Of course, the company had to withdraw the item from the shelves… BUT NOT before I had a chance to snap up THIS!”. At which point he reached under the desk and produced a bog roll. “And what is more, the top 3 scorers in the exam will each get a free sheet – with my compliments”.<\/p>\n

This was, comparatively, one of my highlights of that year.<\/p>\n

I was actually mildly disappointed not to win a sheet. If I ever manage to catch one on eBay it’s going to feel like cheating.<\/p>","protected":false},"excerpt":{"rendered":"

This drama has got it all – art, law, maths, a genius professor\/knight, a multi-national company, a courtroom…[…]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":3,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":""},"categories":[135,134],"tags":[140,141,142,139,137,138,136],"class_list":["post-277","post","type-post","status-publish","format-standard","hentry","category-celf","category-mathemateg","tag-geometry","tag-ip","tag-kleenex","tag-patent","tag-roger-penrose","tag-tiling","tag-tissue"],"yoast_head":"\nPenrose's Patent and the Battle of the Tissue Tiles (Contains Mathematics) - Carl Morris<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/morris.cymru\/en\/2009\/01\/penroses-patent-and-the-battle-of-the-tissue-tiles-contains-mathematics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Penrose's Patent and the Battle of the Tissue Tiles (Contains Mathematics) - 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