The shape that should be impossible.
423,244
Published 2024-06-05
Here is the bonus video with all the details: • Making a dust jacket from an art prin...
See some of you at the Copenhagen Developers Festival, 28 August 2024
cphdevfest.com/
Thanks so much to Paul Catherall who made these beautiful prints. www.paulcatherall.com/
If you order Love Triangle on Waterstones you will not get the dust jacket but you can use the use the discount code 1+2+3+4+5+6=21 to get 21 percent off the already discounted price. www.waterstones.com/book/love-triangle/matt-parker…
All UK options: www.penguin.co.uk/books/443151/love-triangle-by-pa…
All USA options: bit.ly/3wCTesR
Matthias Goerner's page about Sydler's shape: www.unhyperbolic.org/sydler.html
Or see the 3D model directly here: sketchfab.com/3d-models/sydler-pi4-polyhedron-fina…
Henry Segerman's video: • The pi/4 polyhedron
Robin's 15° shape: sketchfab.com/3d-models/single-angle-15-coloured-8…
CONJECTURE DISCLAIMER:
We believe that the "there must exist a single-angle polyhedron for any angle θ with an algebraic sine" conjecture is true but don't have a nice proof. There seem to be all the required parts for the proof in papers by Sydler and Jessen, but it's not fully assembled.
Huge thanks to my Patreon supporters. They keep me orthogonal. www.patreon.com/standupmaths
CORRECTIONS
- None yet, let me know if you spot anything!
Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/books/610964/humble-pi-…
UK book: mathsgear.co.uk/collections/books/products/humble-…
All Comments (21)
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Pro tip: Turn this shape into a fashionable hat to ensure self-driving cars always see you. Awesome Radar signature on that thing.
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sticking the 45 degree angles of two sydler-shapes together creates the most remarkable looking shape without any particularly remarkable properties
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Speaking as someone who was also invented in 1965 I can only say I'm very proud!
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The last step of the original has Rest-of-the-f*cking-owl energy
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Next you'll want to build funny shapes on top of your actual house. A Sydler on the Roof, as it were.
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Sydler really went and made a Parker Polyhedron
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"This is currently my favorite shape" The Klein Bottle can hear you, Matt.
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1:22 Well, personally I see a lot of 180° angles in that shape, you just need to squint right.
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You've betrayed the rhombic dodecahedron! Your wife must be nervous!
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I'm finishing off my PhD and have about 15 references to papers that were all done in french in the 80s... I'm now very good at reading and translating specific french optimal stopping theory...
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Couldve just been calling that one non-right angle a wrong angle. Or if you like, the non square angles could also go by "Parker Square Angles"
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as someone who is often reliant on text to speech to communicate it's really nice to see an interview with someone who (while only circumstantial) also is reliant on these technologies!
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It was really cool to see Robin participate in the video using text to speech. I have some hand injuries I am recovering from still (tendonitis). I am still adjusting to integrating speech to text into my wife and workflow. I wrote this comment using speech to text while my hands were hurting today. Accessibility and representation for the win! Good on Robin for looking out for their health too.
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"What are the newest shapes?" makes sense now. 💀
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A shape made from alright angles and one extraordinary angle...
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Essentially it seems like the key is to remove the second non-right dihedral angle by reducing that edge to a vertex, like the one in the orange shape where 5 faces meet. I have a feeling that if many more people started looking into this we will get a huge assortment of shapes!
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How on earth did he design this shape without having a physical model?! Some people's brains amaze me. I mean, when I was a kid and they were testing me to see if I should be put in gifted classes, one of the areas I scored extremely high in was '2D/3D spatial awareness' but I can barely begin to wrap my head around doing this purely from a theoretical point of view. Unless he didn't even try to keep it in his head and instead did it all mathematically somehow.
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6:27 "As far as we know, the first person to ever make this shape was someone named m-" I expected you to say "Matt Parker" 🤣
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So pleased to see the parker square hanging out there in the background, casually representing giving stuff a go!
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Next step is to get the Sydler-shape used in the UK on road signs to show soccer stadiums!
