I meant what I said: 50k likes and Cookie Clicker video gets made. But I'm pretty sure I'm safe. Maybe we'll find out how many cookies Jane Street will sponsor... www.janestreet.com/join-jane-street/

@creativebuilders1117

11 ай бұрын

1st BTW from what I can tell only 13 of your videos have 50k likes so you're pretty safe. Edit: This will probably age pretty poorly Edit: the video just reached 31,415 views and it has over 6k likes THIS IS NOT LOOKING GOOD

@nicksamek12

11 ай бұрын

I will interact and push the algorithm so we get the likes and the video.

@RickMattison314

11 ай бұрын

I, honestly, would like to know how to mathematically optimize Cookie Clicker, despite not playing myself. Also, there is one game that I would like to know how to optimize farming in, and that is Bloons TD6, which I play a LOT of.

@ectoplasm12345

11 ай бұрын

BEZAN LIKO

@JysusCryst

11 ай бұрын

Don't underestimate Cookie Clicker players. You'll end up making that video for sure! lol

I hope Matt has underestimated how much the community NEEDS a Cookie Clicker video.

@cornonjacob

11 ай бұрын

I haven't played it in years, I will totally go back to it if he makes a video on it. So maybe I don't want him to make that video 😂

@hujackus

11 ай бұрын

🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪👵👵👵👵👵👵👵👵👵🖱️🖱️🖱️🖱️🖱️🖱️🖱️🖱️🖱️🖱️🖱️🖱️🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀

@noemiej.marquis732

11 ай бұрын

This. Cookie Clicker x Matt Parker is like a fever dream you'd think would never happen, it would be so awesome!

@asheep7797

11 ай бұрын

@@hujackus 🕰️🕰️🕰️🕰️🕰️🕰️👨‍💻👨‍💻👨‍💻👨‍💻👨‍💻👨‍💻👨‍💻🧠🧠🧠🧠🧠🧠🧠 (ooh spoiler for the new update) 🙋‍♀️🙋‍♀️🙋‍♀️🙋‍♀️🙋‍♀️🙋‍♀️🙋‍♀️

@Marcel-yu2fw

11 ай бұрын

🍪

There's a definite discontinuity where Matt goes from saying they have to be planar pentagons, to where he makes them very much non-planar. I get why now, but it felt like it was never explained why the rules can be relaxed.

@antanis

11 ай бұрын

It wasn't that the pentagons themselves have to stay entirely planar, but that each face (after folding) has to stay planar. It wasn't explained super clearly but the video was fascinating.

@neopalm2050

11 ай бұрын

Fold lines don't count as curvature, so technically the faces aren't curved. The gauss-bonnet theorem (which gives the second equation i.e. total angle deficit = two full turns) still applies. I do still think it's a bit of a cop-out.

@MH_Binky

11 ай бұрын

Parker planar pentagons

@LeeSmith-cf1vo

11 ай бұрын

I was confused by this for a while too

@KaneYork

11 ай бұрын

Yeah I think the "gluing rules" is what lets you combine multiple together to make a face

This feels like a rare instance where the cardboard objects aren't meant to represent broader mathematical concepts, but rather its literally about what you can do with cardboard pentagons.

I love that it's called a "degenerate" polyhedra, feels like when maths people call a solution "trivial" but it's even more judgemental about it, like you can almost hear the mathematician saying "yeah, i guess, but you *_know_* that's not the answer i was looking for..." 😂😂

@OrigamiMarie

11 ай бұрын

I uttered the phrase "no *you're* a degenerate taco" during this video 😆

@hughcaldwell1034

11 ай бұрын

My favourite bit of judgemental maths jargon is the name for the transition point between a left-handed and a right-handed helix: a perversion.

@Vulcapyro

11 ай бұрын

In the same sense there is the infinite family of polygons (polyhedra, polytopes) whose vertices are all the same point, probably the easiest way of intuiting what degenerate cases mean

@emilyrln

11 ай бұрын

@@hughcaldwell1034 good grief 😂 they could have called it ambidextrous… although that does imply both handednesses (is that a word?), which might not be appropriate.

@lubricustheslippery5028

11 ай бұрын

I am not only missing some properties we would like, I also have some undesirable properties as smelling bad. I am still a degenerate human?

I suppose the question isn't how many polygons exist that have pentagons as surfances, but how many polygons can we make, of which all surfaces can be constructed out of uninterupted pentagons.

@Dithernoise

11 ай бұрын

Then maybe polyhedra whose planar nets can be constructed from regular pentagons?

@amyloriley

11 ай бұрын

@@rosiefay7283 The question remains. Does it also fold in the fourth dimension? Or is the folding of a pentagon just a shadow of a regular pentagon crossing into the fourth dimension which makes it looks like it's folded? 🧐 Nah, it's folded alright. :P

@Elitekross

11 ай бұрын

​@Dithernoise if we visualize the surface of the final polyhedron as a continuous space, where from the perspective of a 2d entity they can't directly perceive the fold, the pentagons would seem continuous.

@Monkey-fv2km

11 ай бұрын

This framing of the question makes me feel a lot less deceived! 😂

@WolfWalrus

11 ай бұрын

I genuinely got so upset at the third one because he didn't end up with a shape with pentagonal faces, which seems like cheating (or at least rules lawyering)

I admire Matt's courage in scoring a bunch of papers straight on the table without any protective surface.

@HunterJE

5 ай бұрын

I mean easy to do with no risk of damage if you use the right tools, there's no need for a blade to get a clean crease line, just need a reasonably narrow edge...

For the past two years, I've taken to wrapping my Christmas gifts in custom boxes of various complex shapes made up of various polygons. The box essentially becomes part of the gift, which makes it fun, especially if the gift itself is otherwise boring or expected. This video has given me some ideas for new gift boxes. Figuring out how to wrap them in paper will be especially interesting, though.

I appreciate how Matt highlights these mathematical papers that we would never see otherwise, describes them in an easy to understand way, and then actually builds the shapes. I doubt with those papers whether any physical copies were made. Bravo Matt for taking something from abstract maths and making it concrete an tangible for all of us. P.S. I feel like the four pentagon ones are a very elegant and simple example of the same net folding into three different shapes. Definitely simpler than any of the constructions in the video about those. They are also all easily seen to be distinct.

I strive to get as much joy in my life as Matt when he sees colored cardboard pieces

@vigilantcosmicpenguin8721

11 ай бұрын

Maybe all you need is colored cardboard pieces.

It's a regular pentagon where regular pentagon is defined as the pentagon that Matt just drew.

@plbster

11 ай бұрын

Parker Pentagon

@dleonidae

11 ай бұрын

Parkergon

@OverkillSD

11 ай бұрын

@@dleonidae No, he's still here :P

@philkensebben157

11 ай бұрын

@@OverkillSD budum tss. Now get out.

@robertthompson3447

11 ай бұрын

I need that on a t-shirt now. The Parker Pentagon. Pretty sure one of the angles is divisible by π.

The subtle difference between a convex polyhedron made by sticking regular pentagons together, and a convex polyhedron with regular pentagonal faces.

Matt, as someone who's clinically conditioned to click cookies continuously, you don't know how much I need a cookie clicker video. (I tried to keep the alliteration going, but I couldn't quite conjure continuing 'c' words.)

@VaguelyCanadian

11 ай бұрын

"you can't comprehend my compulsion for cookie clicker videos" maybe?

@qamarat8366

11 ай бұрын

@@VaguelyCanadian hmmmm "As someone who's clinically conditioned to click cookies continuously, your cavalier comprehension of these cocoa-containing crystals conjures commiseration for your conceitedness."?

@icedo1013

11 ай бұрын

....continuously, critically consider calming my craving and create cookie clicker content to complement your channel!

@HagenvonEitzen

11 ай бұрын

@@icedo1013 Comrads! Cease creating crazy comments!

@hydrocharis1

11 ай бұрын

Clearly, commenters covet cookie cutter commitment.

Of course we want a video on the maths of cookie clicker...

For the trio of names I propose: Hamburger, Hotdog, and Pasty. All ways of holding your meal! If you absolutely need to make them alliterative, may I reluctantly offer “Handwich”. Also I’d love a video on Cookie Clicker!

I always love a Maths & Crafts video from Mr. Parker.

@AsiccAP

11 ай бұрын

Matt & crafts 😂

Wouldn’t bending the pentagon make it multiple other shapes?

@derekcouzens9483

11 ай бұрын

He states the condition 2D pentagons In the first minute. But please investigate relaxing this condition as that is what maths is about.

@word6344

11 ай бұрын

Parker Pentagon

@griffingeode

11 ай бұрын

It's all triangles when you get down to it

@chrisfrancis1346

11 ай бұрын

@@griffingeodetriangles with a 2D Pentagon constraint

@calholli

11 ай бұрын

Yes. Triangles are pentagons now.. deal with it. Called they/them pentagons

I mean... I always like Matt's videos, so it's a no brainer that I'd want to see a Cookie Clicker video, even though until now I'd never heard of such a game.

I think my favorite part of this is that all of the constructions require by definition that the folds join vertices, meaning if you start from a set of regular shapes as you did then all of the folds are simply "fold along the line made by these two vertices". This means that this could become an exercise in classrooms without a lot of hassle, and that's just awesome. I'd have thoroughly enjoyed doing something like this in school.

I feel like this video was the first time I actually grokked external angles. Somehow the definition got stuck in my head without ever actually filling out as a concept. Ah the random holes in our educational journeys, thanks for patching this one!

The 5 polyhedra between the "simple" cases look like they could be really cool jewel shapes. The N=6 also kind of looks like a beautiful heart shaped jewel (if you leave all the faces flat).

It's nice to see Matt's inner 5 year old come out with making colorful construction paper objects. I liked the video. Looking forward to the Cookie Clicker video!

I ABSOLUTELY want a Cookie Clicker video! I usually don't like like-baits like that but that one is just Sooooo worth it!

Plato would probably die instantly if he saw those volumes.

Finally, the long awaited sequel to "Every Strictly-Convex Deltahedron"

Oh man, I was playing Cookie Clicker (thanks to the people on the One True Thread of the xkcd forums) when I was in the middle of moving to Austria, and I’d just been thinking it’s been almost 10 years since then… I hope we get that video.

For some reason videos where Matt folds polygons together to make polyhedra are my favourite 😅. I guess it's just fun seeing them being made. Matt, have you ever thought of making a video on Archimedean and Catalan Solids? The Platonics are everywhere but there aren't really any good videos showcasing these other two groups. I'd be very interested in seeing you construct them and perhaps giving us some fun facts about them. And as a bonus, you get to talk about your favourite dodecahedron!

@molybd3num823

11 ай бұрын

also the kepler-poinsot polyhedra

@killerbee.13

11 ай бұрын

it's also very fun and satisfying to make them yourself. When I was in high school geometry I had a project that involved making a polyhedron out of card paper and I chose a cube glued to one of the square faces of an anticube/uniform square antiprism, and I really liked it and kept it for multiple years. I think the only reason I don't still have it is it got destroyed when I moved at some point.

I'm not a really a fan of Cookie Clicker personally, though I do enjoy idle games of other varieties. Regardless, I would find a video into the math behind the optimisation problem of such games to be extremely interesting, so it has my vote. Can't get enough maths!

@jimi02468

11 ай бұрын

Optimization problems are the most satisfying math problems. Nothing is more satisfying in math than finding the optimal solution to something.

I'd be interested to see a video about self-intersecting polyhedra! I assume you've heard of the video by Jan Misali about the 48 regular polyhedra? I'd be interested to learn more about that topic!

As somebody who makes spreadsheets about games, I'm 100% in for a video about the math for a game.

It's the Parker-Pentagonal-Polyhedron! Much love Matt! Keep it up! I love that you encourage us to give it a go!

As someone with a cookie clicker save file so old that it doesn't even include a "date started" value, yes make that cookie clicker video!

I was expecting this to be similar to Vsauce's video on the 8 convex deltahedra, where he used expansion, snubification, and another little things to generate them, but this was still a pleasant suprise, new ways to turn shapes into other shapes!

Back in the 80s, there were paper kits called Fuse Blocks that folded up into icosahedra sans the faces around one vertex; there were also separate "caps" and "seed blocks" to fill in the gaps. They could make all sorts of fun shapes glued together. I still have an unused pack of them. Good luck trying to find info on them online anywhere...

Jan Misali made a similar video to this called “There are 48 regular polyhedra”. He used different definitions hence the different results but it’s still very interesting

I have never heard of Cookie Clicker, but now I want to see the video on it!!

I commented before Matt Parker saw the typo in the title I guess you could call it a Parker title

@standupmaths

11 ай бұрын

Fixed now! I appreciate all the ways your comment helped.

@cheeseburgermonkey7104

11 ай бұрын

@@standupmaths You're welcome

@josefanon8504

11 ай бұрын

@@standupmaths how many way do you appreciate it though? ;)

@cheeseburgermonkey7104

11 ай бұрын

@@standupmaths It's also interesting how the unique numbers of pentagons in the final polyhedra is just twice the factors of 6 2,4,6,8,12 1,2,3,4,6

I need a cookie clicker optimum strategie guide. Also, I am still in need of an Oregon Trail guide, as well.

You can also make a transformative one out of deceptagons.

Thanks Matt, helps a lot! ..also, looking forward to the cookie cutter video - how exciting

I'd love a video on Descartes's theorem (i.e. the 'missing' angles in a polyhedron adding up to 720°) and its generalization, the Gauss-Bonnet theorem!

I would definitely watch a video on the mathematics of optimising cookie clicker haha

8:41 What a nice Parker regular pentagon! 🤭

10th anniversary of cookies clicker!? Heck yes, I want a video on it!

Of all the videos you've ever made, this one took me the longest to get through. I got REALLY stuck on that first new solid with the two pentagons, stopping and rewinding, advancing frame by frame, trying to figure out how you'd done the folds. I couldn't tell which edges were originally pentagon edges and which were folds... it might have made it easier to see if the pentagons had begun with black marker pen around their edges or something, so that this was more obvious.

To answer a different but related problem: If you have a *cubic map* (a map where *every* vertex is shared by exactly 3 faces, so nothing like the four-corners in the U.S.), then you must have that 4C_2 + 3C_3 + 2C_4 + C_5 - C_7 - 2C_8 - … = 12, where C_k indicates the number of faces enclosed by k edges, including the “outer” face on paper (which of course is just any other face when putting regions on a globe). Note that the coefficient of C_6 is 0, so it doesn’t show up. This demonstrates why, for instance, a soccer ball with only pentagons and hexagons has exactly 12 pentagons.

@thomasblok2120

11 ай бұрын

Ah true, that is an elegant use of the Euler formula for polyhedrons

Parker pentagons is really one the incredible videos have watched today....waiting for the cookie cliker video to drop soon 😊

Love your vidoeos Matt. Making this comment because KZread has stopped recommending me your videos, so I'm reminding it how much i like your content. Thumbed, subbed, commented!

As someone who has been playing cookie clicker on and of since 3255 days ago(8 August 2014, apparently), and is very close to getting all upgrades and achievements(depending on whether or not i ever get a juicy queenbeet), I... NEED that video.

Soooo, given it is missing some qualities we would ideally want, those two back to back is a parker polyhedron?

@rmsgrey

11 ай бұрын

No, it's too mundane a failure.

„These are 2. But I promised 8. Which means there are 6 more.“ That’s exactly the hard, cold maths I‘m watching these videos for.

15:47 “The beautiful square gem” (as @DukeBG calls it) is made of parts I recognize! @standupmaths, it is possible (as you surely know) to embed a cube inside a regular dodecahedron. Each pentagon contributes two nonadjacent corners and the connecting diagonal to the cube. You can follow four of these connecting diagonals across four pentagons to identify one of the square faces of the cube. If you slice the dodecahedron along the plane of that square, the smaller piece that comes off is (what a friend of mine called) a little “roof“ that’s made of two obtuse triangles and two trapezoids - plus a square base. So now I see that it appears if you take two of those “roof“ shapes and attach them to each other on their square faces, with an angle of 90° between the top of one roof, and the top of the other roof, this looks to me to be the shape you pasted together whose beauty caught your eye! 😸

Matt wants people to stop prefixing foolish things with Parker, but then he goes on ahead to create a Parker Pentagon at the start of the video 😂

If you allow concave polyhedra then you can trivially make infinitely many chains of platonic dodecahedra.

8:40 Behold! The Parker Pentagon!

Magnificent video. Thank you :)

I always love it when the rhombic dodecahedron makes an appearance as it’s been one of my 3 favorite Polyhedra for many years. The other two being the standard tetrahedron and the stellated icosahedron

@17thstellation

11 ай бұрын

I'm a fan of Escher's solid. It's pretty just aesthetically, but it's also got wacky properties. You can get it not only by stellating the rhombic dodecahedron, but also by augmenting it at a height equal to the distance from the midpoint of each face to the center, just like the rhombic dodecahedron itself can be derived by augmenting a cube in the same way. It can also be derived as a compound of three non-regular octahedra. And it does the last thing you'd expect from such a crazy, spiky shape; it keeps its base shape's property of TESSELLATING space. Also in the right orientation, each of its normals lie exactly halfway between two cardinal axes, making it probably the coolest shape you can easily build in Minecraft.

@dominicpancella3012

11 ай бұрын

I've got a paper stellated icosahedron in my room that I made in my high school geometry class :)

@PrincessPolyhedra

11 ай бұрын

@@dominicpancella3012 I make those on occasion for fun. I also sometimes make the much larger like 900 piece ball with the same pieces (model it after a soccer ball with hexagons surrounded by pentagons)

@robertunderwood1011

2 ай бұрын

If we had our collection of regular dodecahedra and joined them face-to-face along a circular path, could we then have a torus made entirely of planner pentagons joined along their edges?

I need the cookie clicker video so badly!!!!

This is so cool, thanks for the video

Please do a Cookie Clicker video!!! I've been playing for about a year now and I'd be curious what the optimal strats are.

At first, folding looked like cheating, but then it actually turned out quite fun and interesting) thank you

@DontYouDareToCallMePolisz

10 ай бұрын

Русский замечен

The parallelepiped ("hot dog") tiles 3-space, right? Any chance you might make an "infinity lamp" of this polyhedron like you and Adam Savage did with the rhombic dodecahedron?

@citybadger

11 ай бұрын

The hot dog is just a skewed cube.

@ryancrawford4130

11 ай бұрын

@@citybadger I'm unaware of a difference between a "skewed cube" and a parallelepiped. It also happens to be the way the solid is described in the paper.

I love the pattern he has on the 5x5 cibe on top shelf. I developed that independently after learning how to solve cubes while away from the internet, love seeing other people give that pattern some representation.

i think those would make really cool 3d-models for gems or crystals in video games

Currently at 100 quadrillion cookies per second. I love me some cookie clicker 🍪

So what's the difference between scoring then folding a polygon and cutting it apart into several polygons and gluing them together to make a polyhedron? At least physically, it seems not like pentagons joined together, but other polygons that together could be assembled to pentagons in the Euclidean plane.

@thepizzaguy8477

11 ай бұрын

The fact they fold means that there is still a restriction, by deconstructing the pentagon you are instead just constructing with triangles, unrestricted. It would expand what is possible by a lot, to things that would not be possible without cutting

@noone-ld7pt

11 ай бұрын

I mean that's the design restraint which makes the problem interesting. Of course you could break all of it down to each face and just cut up Pentagons up to make them. But having the rules of each face having to be a part of an original regular pentagon and then glued to another side of equal length that is also a part of a pentagon sets strict rules for what the final shapes can actually be. But I think the real beauty is in the uniqueness he revealed at the end; that the pentagon is the only regular polygon that has a finite solution set which isn't either completely degenerate (heptagons or bigger), or infinite solutions (hexagons, squares and triangles i.e. shapes that tile the plane). And I personally really like when a problem has an unexpected result that mathematically shows that something is unique. In this case that a pentagon is the *only* regular polygon that can fit three around a vertix while not tiling the plain.

@Starwort

11 ай бұрын

The net is constructible from pentagons is the difference

@martinkauppinen

11 ай бұрын

@@noone-ld7pt Thanks! I wasn't saying that the problem was without merit at all, there was just something about folding pentagons and still claiming the resulting polyhedra to be made out of pentagons that rubbed me the wrong way. Your comment made the interesting part click better.

@martinkauppinen

11 ай бұрын

@@Starwort That's a great, succinct way of putting it. Thanks!

Crafts with Matt. I need more of this.

When I played the Cookie Clicker, I always wondered what would be the optimal strategy to get the most cookies in a given amount of time. We definitely need the Cookie Clicker video.

8:42 Parker Pentagon

@cheeseburgermonkey7104

11 ай бұрын

Parker Pentagon

⁠At 19:18 you say that for polygons with odd vertices you can make degenerate tacos, when you should have said polygons with even vertices

Good on you Matt, love your videos mate

I have never, ever heard of Cookie Clicker until now - and I've been online since 1995. I liked this video anyway so that I can find out more :)

I don't get why the degenerative taco (folding a pentagon across a symmerty line and glue it together) doesn't count.

@bluewales73

11 ай бұрын

For a pentagon, the taco has to fold across the middle of an edge. The rules the paper's authors used only allows folds from corner to corner. You can make degenerative tacos with shapes with an even number of sides because you can draw a line of symmetry from one corner to another.

Poor degenerate Polyhedron, he definitely is my favourite

Some really interesting shapes there!

I love how infectious his excitement for maths is! Been hooked for years

Me understanding half of what he says but still listening because it makes me feel smarter

C'mon guys lets put our cookie clicker skills to use, click that like button.

I really appreciate how _nice_ those shapes are. This gives me a newfound appreciation for pentagons.

i've yet to watch this past the first few seconds, but i know this will be right up my alley.

Heya, i was thinking of this channel yesterday when i heard of a new kind of number "dedekind" numbers. there was some new discovery or one and i literally cant get my head around them and thought "i hope Stand-Up Maths sees this news and does a piece on them" cause you one of the only channels able to explain complex number stuff in a way my thick head understands lol

@drdca8263

11 ай бұрын

Are you referring to the dedekind construction of the real numbers, or to something else?

It's not really a pentagon any more if you fold it is it? I mean it just becomes a bunch of triangles. Totally cheating.

10000000000% YES I want a Cookie Clicker video!

Clicked too fast to even see the thumbnail so I get the bonus of all the shapes being unexpected.

I NEED THAT COOKIE CLICKER VIDEO

i've never played cookie clicker but i'm big into games and id be so hyped to see a cookie clicker video! would be legendary

Relaxing the convex requirement gives you some lovely ones like the great dodecahedron

YES PLEASE GIVE US THE COOKIE CLICKER VIDEO

Folding these pentagons seems like bending the rules of what we normally assume (flatness). Now we have triangles or trapezoids instead of original pentagons.

@PopeGoliath

11 ай бұрын

If it helps, you can imagine the question being "how many shapes can be made from regular pentagonal nets?" Just like you can make a cube from a cross-shaped net, he's exploring what can be made from exclusively pentagonal nets.

I am so excited to learn about Cookies!

The Demaine's and origmai math in general is an amazing subject. I first got interested in folding polyhedra from John Motroll's books; single, square sheets of uncut, unglued paper to make a bewildering number of all types of polyhedra.

I understood the paper and tape part. But you lost me on the whiteboard 😂

Epic demo of algebra's connection with geometry. Very cool.

That's like when in second grade teacher asked if there is a shape with 4 edges and 3 corners and I confidently said yes and drew on a blackboard a square with one corner rounded

Omg yes, a Cookie Clicker video would be amazing!

Please make the Cookie Clicker video happen, people. Do your part!

I love your videos, Matt! Your passion for math is fantastic and infectious and I wish I'd had more math teachers like you in school. One potential correction: At 8:00, you mention that "...and x is always 3" when you meant to say "... and zed is always 3". The text on the board is correct, it was just a simple slip of the tongue. And I'm doing my part for the Cookie Clicker video!

Ahhhh matt noooo now I need the duals of each of these 😂😂

This right here is why I watch Matt Parker.

We proudly present to you: the Parker pentagon. ❤