Making efficient Platonic and Archimedean shapes in a kaleidoscope

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Sign up on Patreon for the SUM xmas card! / standupmaths If you want the physical card you need to be greater than or equal to "Statistically Significant".
Physical card deadline: end of 06 December 2022
Digital card deadline: end of 15 December 2022
(In both cases I'll try to accommodate sign-ups after that but no promises).
This is why the christmas tree on the card is so low resolution: • Can the Same Net Fold ...
Here is the "Deltoidal kaleidoscopes" paper by Josep Rey Nadal and Manuel Udina Abelló.
archive.bridgesmathart.org/20...
Museu de Matemàtiques de Catalunya aka "Museum of Mathematics of Catalonia" mmaca.cat/en/
This is the art show listing from the 2022 Bridges conference in Helsinki. gallery.bridgesmathart.org/exh...
For both kaleidoscopes make two mirror images of each shape.
Deltoidal Hexacontahedron Kaleidoscope Faces: www.dropbox.com/s/9tltpyo4v6k...
Deltoidal Icositetrahedron Kaleidoscope Faces: www.dropbox.com/s/jb356rspfn5...
Here is the second channel video from 2017: "How to flat-pack a cube" • How to flat-pack a cube
Huge thanks to my Patreon supporters who funded so many sheets of mirror acrylic. I actually have a bunch left over. Support me and tell me what I should do with the rest of the mirrors. / standupmaths
CORRECTIONS
- None yet, let me know if you spot anything! My bad taping skills do not count as a mistake.
Filming and editing by Alex Genn-Bash
Shape calculations by Sam Hartburn
Written and performed by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

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5 дек 2022

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Комментарии : 532

@estherstreet4582 Год назад

Imagine this hanging from the ceiling with the mirror acting like a "lampshade" and a bright neon tube light forming the shape, it would be such a cool light

@hughcaldwell1034 Год назад

Absolutely going to try making something like this for my bedroom. My partner is bed-bound and we're both big maths nerds. Something like this would be a really awesome addition to the room, I think.

@joemyers5302 Год назад

Could it be done if you make the walls out of mirrors?

@gabor6259 Год назад

@@hughcaldwell1034 "We're both big math nerds." Ah, the perfect relationship.

@airplanes_aren.t_real Год назад

@@hughcaldwell1034 good luck, hope you have fun

@MrPeetersmark Год назад

You can use one way mirror. It reflects but it’s see through.

@Ryan-in3ot Год назад

i can't believe matt's room isn't lagging with all of that real time recursive rendering

@00Krohnos Год назад

His room is actually a fractal, which GPUs are extremely at fast at rendering - even in 3D!

@stickmcskunky4345 3 месяца назад

@@00Krohnos.. when you say something potentially profoundly true in the guise of a bit

@stickmcskunky4345 3 месяца назад

There's mad lag, the brain just edits it out

@robertthompson3447 Год назад

Matt: This is like a kaleidoscope but much more precise. Also Matt: I cut this myself with a jigsaw.

@airplanes_aren.t_real Год назад

Precision may need sacrifice

@Jason-sq2up Год назад

I thought he was saying kaleidoscopes are more precise

@strehlow Год назад

Measure with a micrometer. Mark with chalk. Cut with an axe.

@NicolaiParsons Год назад

It's a Parker kaleidoscope!

@pyglik2296 Год назад

Actually he says "[...] much more precise, give or take.", so... he's not actually saying that it is more precise...

@AlRoderick Год назад

This reminds me of an idea I had for an artificial Christmas tree that's just a quarter of a tree, the idea being that you stick it in a corner between two mirrors so it looks like a whole tree but using a quarter of the floor space, materials and lights. I guess you'd call it a symetree?

@chaos.corner Год назад

This would be great. If you could make a tree that folded up if you pushed the mirrors together, that would be even better.

@kyokoyumi Год назад

@@chaos.corner Like a pop-up book

@chaos.corner Год назад

@@kyokoyumi I'd thought maybe that for different holidays but you'd need multiple layers of mirrors I'd think. Though there might be a way. But yes.

@bathbomber Год назад

You should patent and sell this idea!

@MrMartinSchou Год назад

And you can have lots of fun by having people try to dance around it.

@JohnHollowell Год назад

I think the main issue with your mirrors is that they are rear-surface mirrors so there is a acrylic-width gap in your edges which adds an offset to all the other reflections. A first-surface mirror would work a lot better I would think.

@XMarkxyz Год назад

How cool it would be with some aluminized material

@rhamph Год назад

@@XMarkxyz The extra reflectivity of silver would be dramatically better here due to the repeated reflections. Finding a suitable material at a reasonable price is the real challenge though.

@bentfishbowl3945 Год назад

Or maybe just miter the edges with a file?

@RonParker Год назад

@@rhamph It used to be fairly easy to get glass first-surface mirrors from discarded microfiche readers and laser printers, but it's gotten harder to find suitable donors. You can also make your own mirrors with suitable chemicals. If you live in the US you can get a kit from Angel Gilding. (I work with leaded glass, so I've had their site bookmarked for years, but I've yet to actually buy one of their kits.)

@CheaterCodes Год назад

I think the best results would be achieved with a solid-glass pyramid with reflective coating on the outside. On the inside you would then have seamless first surface mirrors, but they are still protected by the glass

@stevemonkey6666 Год назад

Matt's joy at this is palpable

@quamrana Год назад

Yes, I loved the 'Happy Matt' face!

@vigilantcosmicpenguin8721 Год назад

And contagious.

@jessicadaugherty9011 Год назад

This is the best!

@alexandermcclureidrinkoliv3663 Год назад

*P*otent, *P*ungent, *P*alpable joy at the sheer mathematics. (pretend those P's are bold instead of surrounded)

@idontwantahandlethough Год назад

I love that the premise assumes, without question, that one absolutely NEEEEEEDS to carry their cubeyboi with them everywhere they go.

@totoshampoin Год назад

... you don't?

@toxicara Год назад

Matt should have called this "how to please mathematicians with shiny things"

@angeldude101 Год назад

Only mathematicians? What kind of monsters are these "non-mathematicians" who _don't_ like shiny things?

@jinclay4354 Год назад

@@angeldude101 Well, non-mathematicians might look at this and say "Ooo, pretty!", but only mathematicians will, after saying that, ask "How does it work?".

@bencheevers6693 Год назад

I have to admit after Matt said "you're just going to have to trust me" I figured he already knew that it wouldn't really turn out on video so he was bracing us for that not to expect much and that just floored me at the end how well it worked, really quite a good trick Matt

@thealmightyduck335 Год назад

Seeing Matt get so incredibly giddy over shapes and reflections will always make me smile :)

@johnchessant3012 Год назад

8:34 Fun fact: The entrance to MoMath is a glass cube where a regular hexagonal slice dividing the cube exactly in half is drawn in red.

@miorioff Год назад

Every time Matt is saying something like "it's not perfect... but it's not bad... it's working....?" I'm like... it's Parker Square again isn't it? 🤣

@ericgoldman7533 Год назад

Damn skippy! Matt is, after all, the patron saint of "giving it a go"

@NanoMan737400 Год назад

Parker Cube this time, he's now growing in power!

@toxicara Год назад

the parkaleidescope, YES!

@afrophoenix3111 Год назад

Parker Symmetry

@Phriedah Год назад

as they say, perfect is the enemy of progress. I love his 90% executions. Feels very real.

@dylanlasky2389 Год назад

That glowstick part was the clearest and coolest by far

@tomadil331 Год назад

As someone from a country as tiny as Catalunya I can't even begin to express the shock of watching yet another english video, seeing it mention a study from catalan mathematicians and then transition into a museum in a town minutes away from yours. It's like if your parents were to suddenly appear in the video.

@CarMedicine Год назад

Small correction: Catalunya (or "Catalonia" as the English say) isn't a country, it's part of Spain, but yeah it's very cool to have some English video mention where we live. (i also live in Catalunya)

@EmyrDerfel Год назад

@@CarMedicine You're expressing an opinion as fact. You and Tom evidently don't agree.

@CarMedicine Год назад

@@EmyrDerfel wut? it isn't an opinion. If it was, then saying "Brazil is a region of Japan." would also be an opinion. It isn't, it's just wrong.

@tomadil331 Год назад

@@CarMedicine I particularly chose the word "country" because it's certainly not self-governed, hence it's not a "state", but I recognise its diffenenciated language and culture as characteristics for a "nation". It's like the USA, but instead of being a huge country divided into smaller states it's a big state containing some countries (like Euskadi, Galícia or the País Valencià), which happens all over Europe because the cultures spread more slowly than in America. Anyway, it depends a lot on what meaning you attribute to the word "country"😄

@CarMedicine Год назад

@@tomadil331 buddy, the term "comunidad/tat autó/ònoma" (autonomous community) exists for a reason.

@SotS1689 Год назад

Who knew being a mathematician would also require pro status at arts and crafts? As always, very well done.

@Toobula Год назад

I knew a guy years ago who built these, but much larger so that you could stick your head down in there. He also put lights along the edges. The thing he did that Matt could have done here, is put a final rectangular mirror in the bottom. Then when you look in, you will not just see an icosahedron made out of wooden desk, but one with your face looking out of all the faces. It's amazing.

@sachiperez Год назад

Such a cool feeling when the brain forgets about the mirrors and just sees the object!

@derekhasabrain Год назад

Matt I am so grateful you have a RU-vid channel. I remember my young self in middle school watching numberphile videos because I didn’t have many friends but I was passionate about math and it made me feel better seeing that other people were passionate about math as well. Here I am, about 10 years later, still watching my parasocial buddy Matt Parker Parkering his way through the world like me. Thank you for doing this

@JalebJay Год назад

The ending got me in awe. One of the coolest ideas I've seen.

@Macieks300 Год назад

5:03 wouldn't be a Matt Parker video without the classic "just give it a go"😆

@FishSticker Год назад

THE ENDING WAS PERFECT

@Dreju78 Год назад

Is this a ploy to make me watch to the very end?!😁

@FishSticker Год назад

@@Dreju78 it's a Matt Parker video, you should always watch to the very end

@pseudo_goose Год назад

This makes me want to build a raytracer to emulate these kaleidoscopes! I think that would be a really cool way to experience this without having to build it.

@torridice Год назад

The level of joy displayed in this video is infectious. ❤️

@JHaven-lg7lj Год назад

When you dropped the glow stick in and just looked at it without saying anything I thought “He’s SO happy right now” which you immediately confirmed. Thank you, awesome video

@nnanob3694 Год назад

It's really cool to see the shape and its dual in the same kaleidoscopic mirror! (Also: rhombic dodecahedron is the bestahedron)

@ARKGAMING Год назад

16:12 Matt's face here show how much fun he's having and it's amazing

@killerbee.13 Год назад

This is honestly a great demonstration of the idea of a dual shape, makes it a lot clearer than a lot of other things I've seen on the same subject.

@mczs Год назад

Matt that last experiment is utterly amazing! Thank you for showing us this!!

@lrwerewolf Год назад

Love that he immediately went to the bestagon. Also, love seeing him use half the dual of a cube to convert a single plane into a full cube.

@incription Год назад

Hey Matt, you should experiment with acrylic one way mirrors. If you cover a cube in this surface, the internal rays will bounce around the interior, creating the effect of an "infinite world" within the cube, like a wormhole.. You can exaggerate this effect with LED strips along the sides. Look up "LED Hypercube"

@freescape08 Год назад

I like where you’re going with this, but instead of a regular hyper cube, what about a condensed hyper cube? Do what Matt did, but with clear acrylic on the outside ‘surface’ of the shape, to reflect another shape off of each reflected surface that’s visible on the far side of the main shape.

@99parkerj Год назад

Matt has done something like this before (with Adam Savage from Mythbusters): ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-65r_1TzJXaQ.html

@incription Год назад

@@99parkerj DO IT AGAIN!

@TheLostSorcerer Год назад

I believe he has already done that with Adam Savage. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-65r_1TzJXaQ.html

@RomanQrr Год назад

If I remember correctly Matt and Adam Savage of Mythbusters fame already did make one of the "infinite" shapes.

@W9e0e2e3e4pizza Год назад

The glow in the dark shapes are absolutely incredible! I feel like these could be made into some sort of decorations for Halloween or something....

@danielcarter6178 Год назад

This whole deal with constructing polytopes from kaleidoscopes is basically what Coxeter-Dynkin diagrams are. You will surely run across these diagrams if you look at Wikipedia pages on polytopes; they have nodes and edges and sometimes some numbers. Each node represents a mirror, and edges represent angles between mirrors. An unlabeled edge means to attach them at a 60 degree angle, an edge labeled "4" means a 45 degree angle, and "5" means a 36 degree angle. This is extended by putting circles around some of the nodes. This notation basically describes putting different things into the kaleidoscope to get different polytopes out. In the case of polyhedra, there are 3 nodes, and at least one node must be circled (otherwise you get a single point), so you get 2^3 - 1 = 7 polyhedra from any kaleidoscope. The keyword to look up here is "Wythoff construction." In the case of Matt's cube kaleidoscope, the 7 polyhedra you get are the cube, truncated cube, octahedron, truncated octahedron, cuboctahedron, truncated cuboctahedron, and rhombicuboctahedron. There are some extensions that decorate the nodes in other ways that can get you the rhombic dodecahedron and other shapes.

@omaanshkaushal3522 Год назад

If you could basically see it all at once, inside the kaleidoscope, it would be so much more dope than it is right now. Matt knows how to get his viewers to love Math

@airplanes_aren.t_real Год назад

Sounds like a map in a vr world

@widicamdotnet Год назад

They would've just needed to film it up-close with an extreme wide-angle lens (fisheye or so) to get the entire shape into view - closer to what you'd see if you held it up to your face.

@rohitraghunathan Год назад

"Like a kaleidoscope, but much more precise... Give or take" - Matt Parker, Dec 2022

@twertygo Год назад

How have we deserved so many videos in such a short time ❤️

@BeheadedKamikaze Год назад

I am not yet convinced we deserve it. But I needed it ❤

@NevinBR Год назад

If you set the angle on your saw to half the angle between adjacent faces (this might be different for each pair of faces), then the seams where the mirrors meet will line up flush. You could even glue them on those edges if you’re careful.

@SpeckyYT Год назад

I entered the premiere and it was literally at 5 seconds left

@krissp8712 Год назад

I did wonder if it was a premiere, on mobile I had to bring up the pause overlay to confirm lol

@asheep7797 Год назад

i came 9 minutes late

@lichtenshtein345 Год назад

Bro wtf same exactly 5 seconds

@jqsm1neS Год назад

Lmao genuinely same

@veggiet2009 Год назад

I really dislike premieres for this reason, as I never seem to join at the right time, I have to rewind for a weird amount of time, and then fast forward through the countdown... I would just rather stop and wait for the premier to be over

@mctuble Год назад

I have to tell you I love your child like curiosity and your ability and the means to follow through on taking these experiments to the next level. Keep up the great work! Look forward to every one of your videos

@donnerflieger3770 Год назад

I really like Matt discovering cubic symmetries. Really important in crystallography. I like how he made the minimal possible cell of F 4/m -3 2/m

@vigilantcosmicpenguin8721 Год назад

I've never considered what a maths rave would be like but now I feel like that has to be a thing.

@AlexanderTBratrich Год назад

Matt keeps confirming to me that Math(s)-people really like to play with things a lot. My old math teacher always did that (and I mean, it makes geometry even more fun than it already is!)

@ronm3245 Год назад

I'm an old math teacher and I approve this message.

@IonicFox2nd Год назад

Something about this topic seemed familiar, then I remembered that Matt was in an episode of Adam Savage's Tested where they built a similar object with light strips. Such a cool idea for a project. Makes we want to do one myself.

@hashtagPoundsign Год назад

What I love most about your project videos is that you make them very accessible, so that just about anyone can give it a go. On another note, you could make it as an infinity mirror with an led strip as the portion of the cube.

@lewismassie Год назад

Might be interesting to set some of these up in Blender, should be pretty easy plus the fact that the mirrors can let you see through them from the back like you were trying with the two-way mirrors. I was trying to make a true portal effect and stumbled across this exact thing by accident

@LeavingGoose046 Год назад

L to whatever gpu tries this

@lewismassie Год назад

@@LeavingGoose046 I mean I was using a 960M (yes really) and it was okay so long as I hard capped the light bounces

@Spartacus005 Год назад

Hi Alex! Unsung hero of this channel

@lunarmare0 Год назад

Hi Matt. Just wanted to let you know I listen to your videos, whilst for entertainment, but also sometimes as background noise whilst working on university studies. Your voice is really soothing. Thanks

@mal2ksc Год назад

You can get cleaner edges on acrylic by scratching a line into the surface (a ruler and X-Acto knife will be fine), and then breaking it.

@andersgleich4717 2 месяца назад

WOW!... just on a trip following the idea of building trippy visualizations also in kaleidocope ways... it really made me happy when u replaced the mirrors with real ones... and it made me party hard when you took the glowlights. just what i hoped to see.. thx for making the builds and sharing the templates

@K-o-R Год назад

0:36 "Through the magic of -buying- making two of them...!"

@RoyEltham Год назад

You looked so pleased! It definitely is pleasing. The end bit with the glow sticks was deluxe!

@randy7894 Год назад

A spectacular finale Matt!

@Kranzio- Год назад

“I will admit it’s not perfect; it’s not bad. Has a few flaws.” -The Parker Credo

@KiloOscarZulu Год назад

I never thought maths rave would be a thing. But here it is!

@vitor-muzulon Год назад

I just wanna point out to Matt that here in London, in the Grosvenor Square, there is an infinite mirror Rhombic Dodecahedron sculpture, like the one you made with Adam Savage

@airplanes_aren.t_real Год назад

Just saw it, it's beautiful

@SineEyed Год назад

There's a company that makes a deltoidal hexacontahedron infinity mirror sculpture which has high density rgb led strips lining all the interior edges. I think its about 1.5m diameter. This thing turned on might be the coolest thing you've ever seen..

@airplanes_aren.t_real Год назад

@@SineEyed what's the company

@petrsokol588 Год назад

I mean it's really important that you just show us that this concept exists! That's a totally valid contribution. I'd have never known this existed, yet it is so cool!!!!

@arielioffe1810 Год назад

i’ve never taken that much time to appreciate the music on this channel

@jakobchang9781 Год назад

It's funny how the platonic solids are just being good friends while the archimedean ones are trying to screw you.

@williamberman5978 Год назад

Nobody tell this guy about the Johnson solids

@Xxyter2 Год назад

3 videos in 2 weeks? You're too good to us, Matt.

@GuybrushThreepwoodNZ Год назад

Superb maths and art mashup Matt! Thanks for the inspirational content.

@kayleighlehrman9566 4 месяца назад

"Much more precise, give or take" What a phrase, Matt lol

@curiositeperpetuelle8610 Год назад

That IS sooo beautiful, even your joy is lovely ^^

@gunagunter7367 Год назад

Really great ideas. Ive been playing with the platonic solids with wires and strings. this just makes it all easier on reflection

@davidg5898 Год назад

The 2-way mirror part at the end reminds me of an art installation, "N-Light Membrane" by design collective Numen/For Use. Except instead of manipulating symmetries, it would deform some of the sides with air pressure (making them convex or concave) to turn an infinite cubical lattice into varying degrees of infinite curved lattices.

@arielioffe1810 Год назад

whoever did this re-interpretation of the thene song did a very good job

@OrangeC7 Год назад

Imagine a version of this where you have those thin mirrors where you can shine light through to the other side, then you can build the one that does multiple shapes and just have displays directly behind the mirrors that shine the outline of the shape into the kaleidoscope

@reidflemingworldstoughestm1394 Год назад

You had me at running the numbers.

@belgaer4943 Год назад

The visuals at the end are so otherworldly and stunning

@paulzagieboylo7315 Год назад

I'm amazed at how well this works. Although everything that Matt describes as a "snub cube" is actually a cuboctahedron. You can get a snub cube this way but it's more complicated, you need one of the funny-shaped wooden inserts.

@ultimate0levels Год назад

7:50 if each line is 1/8th of the circumference of a face, 24 lines make the entire cube, not 48.

@thomilo44 Год назад

seconded

@airplanes_aren.t_real Год назад

So each line is ¼?

@theofficialczex1708 Год назад

@@airplanes_aren.t_real Each line is 1/8th of a face, but the faces have coincident edges.

@quirkbird1713 Год назад

This pure joy of an adult playing with kid's stuff deeply resonates with me. Kid's stuff, thats actually pretty complex and fascinating on second look.

@jonprudhomme7694 Год назад

Love the genuine enthusiasm 😍

@guillermonassercibils6538 Год назад

THAT IS AWESOME! Also i just love your signature music

@bloodypommelstudios7144 Год назад

The ending was really awesome.

@ColemanMulkerin Год назад

This makes me unusually happy to see. I would like more videos on these constructions.

@BeheadedKamikaze Год назад

That was exceptionally cool Matt! Well done ❤

@derrickobara6806 Год назад

Really enjoying the musical crafts breakdown interludes of late.

@alexanderreusens7633 Год назад

The use of glow stick was genius!

@laser8389 Год назад

I was not prepared for the lights-out version to be so cool!

@melody3741 Год назад

"Matt gives a cube a kaleidoscopy"

@JustinDrentlaw 8 месяцев назад

That is super cool at the end! I wanna build one now!

@CyrusMackie Год назад

Absolutely beautiful

@Tyrope Год назад

Okay that orange/blue one was awesome and I want twenty of them to light up my house with.

@chayam5904 Год назад

Loved the rave!!! I’m so happy to enjoy maths with other people who are excited as me about it 😅

@Gbriel1234567890 Год назад

You made it look super cool too!

@d3j4v00 Год назад

The outro music finally got the glow stick light show it's always wanted!

@OliveHavre Год назад

Incredible ending

@jannegrey593 Год назад

Kaleidoscopes always fascinated me as a kid. I'm looking forward to this video. I'm sure I will enjoy it.

@sannekimenai639 Год назад

I felt that ultimate joy at the glowsticks even through the screen!

@TotemStorms Год назад

Very much enjoying that Matt's practise with Adam Savage was put to good use. When do we get to see the infinity mirror that Adam said he would be sending over?

@jamesonhardy2126 Год назад

19:19 That reveal was top notch.

@robertpearce8394 Год назад

Disco never dies.

@Mecharnie_Dobbs Год назад

To more precisely position each mirror, you could use screws. Any object can be positioned in 3D space via height, depth (away), transverse, yaw, pitch and roll. 6 adjustable screws for each of the 3 or 4 mirrors. 3 of the directions for each mirror involve varying the distance between 2 objects (each) , whereas the other 3 involve varying the rotational alignment between two objects (each) using precise gears like indirectly moving the hour-hand of a clock, by directly moving the second hand.