stages of grief with sqrt(2): - blissful ignorance - annoyence - deep hate and giving up - finding that it actually can be done, if you're creative enough - joy, pride, love sqrt(2)
@@mitchhak2 it should be 2 if I'm not wrong since in Taxicab distance, a metric invented for Minecraft purposes, moving one on diagonal means having to move 1 on X and 1 on Y, there are no diagonals in Minecraft. Manhattan, I was for saying "Mahanttan", my bad. Loving to see my inputs (maybe others said it tho) come back across the new contents!
The Jazz Club set has a section at 45deg. It uses 4558957 on a 4517986. That is built up to provide 2 studs that connect to the regular grid (the building wall at a separatable level) via two long tile pieces. See page 109-113.
My eyes went big when I saw what you were doing with your adjustable angle technique. I stopped what I was doing, and it was amazing. And yes, please show an example of this technique on a Mils build. I’d like to see something of a semi-finished 32x32 section that would show off the true 45 of a building interacting with another building perhaps, or a fence etc. maybe a corner tower that’s at 45? Whatever you might come up with, your curiosity is a breath of fresh air, and I thank you.
Love this, especially the clips-with-bars technique. You do skip over some of the more simple ways Lego uses. 1: The angle plate (cursed piece #1) works fine if you just need a short-ish wall. It does have 4 studs, so is quite strong, AND the side lines up perfectly with a 45° wedge plate. 2: You can put something on a single stud (with hole) or a turntable and just limit its movement. Café Corner is the set I remember pioneering this. Corner Garage uses a technique similar to the one you show with rounded 2x1 plates, but not in parallel, which restrict the movement, and fills the gaps with 1x1 double slopes (which have a 45°-ish angle). The Botanicals use quite a few techniques to attach one or two stud-wide parts at 45°. One strong variant I can think of: using technic 45° angle connectors combined with bricks (1x1 or 1x2) with axle holes on both sides. For a challenge: Fill a half-brick gap (So one brick on the grid, the other on jumpers) between two bricks perfectly. The only way I currently know (I think, I haven't done the math) is very clunky and requires a gap with a height of 4 studs. A Technic 1x2 half-width lift-arm works for a height of two studs, but is a pain to attach and you can see the rounded edges.
Thank you for this video first of all! Some math here: 15:20 The distance between the corners of the dark bley tiles is mathematically slightly below 10 studs, 9.9 or more precise SQRT(98). But tiles are slightly rounded, so this works out. With the round plates at opposite ends of the white structure there is even more room than legally needed. The distance between the centers of the round plates is 15 studs, this is the same as the hypothenuse of a 45deg triangle with rectangular side of about 10.6. This is slightly nor than the required 10.5. I also want to mention a building technique I have once used, but which is quite complicated. Using 45deg technical connectors #4 (part 32192). One could build some framework with axles and technic brick with axle holes where two exactly 45deg grids could be connected. Due to the possibility of sliding axles a little bit this is possible.
Thank you! I don't dabble in technic much but as you mention technic could definitely add some 45 degree angles. For some reason I always favor figuring it out with plate and bricks lol.
Wow those are some excellent techniques! Thanks for sharing! Sqrt(2) has vexed me as a builder since as far back as I can remember. So it’s awesome to see you take it on! One of my fave techniques for getting 45 degree walls is the technique used to build the front wall of the flame yellowish-orange museum portion of ninjago city gardens. It’s achieved by attaching a row of piece 35464 with vertical snot connections along the two sides of the wall in question, then locking the assembly into the structure with modified rail plates, I recommend checking it out if you’ve never seen it before, it’s pretty clever!
I'm not a builder but I enjoy your videos, and as a programmer I can see the sweat and tears into making the impossible work ☺ Big kudos for you imagination and dedication!
Attach a turntable to a 2 x 2 plate with pinhole (part 2817), and you can slide the plate along an axle. A few of these assemblies will get you any angle you want.
Excellent video, Chris! Building on your 45 degree wall idea with your clips and bars, you can use a 1x2 or a 1x2x5 brick with the vertical groove in the center, and finish off, change directions at the ends of your 45 degree wall. I hope I said that so you will understand my idea. I love that clip technique!
I think one of the videos you should make next would talk about the 1/4th plate. Since the length of 1 stud is 2.5 plates, and brackets are .5 plates, there are times where we can get .25 plates like with a jumper or a clip in the middle of a brick. They’re kind of annoying to work with but it could be important to point them out. I needed to deal with them a lot in one of my recent MOCs
The only part I know of with a natural connection that creates a 1/4 plate gap is 4081a (NOT the modern one 4081b) this thinner ring is exactly 1/4 plates thick, though clunky to use in a build
@ yes I’ve noticed that too. It also reminds me that the half lift arm has it aswell because it’s half of 2.5 = 1.25 which is helpful and annoying in some cases.
It's actually possible to build at 1/8th the thickness of a plate and even smaller. But it is not easy and I am not good at it. Luca Hermann is a master of it.
Numbers of the form n+m\sqrt{2}, with n and m integers, are dense in the real line, which means one can find integer multiples of \sqrt{2} arbitrarily close to their nearest integer. Practically, this means if you had a sufficiently large enough wall, the turntable approach would work provided the wall is long enough that the error between the length of the diagonal and its nearest integer is within the tolerances of Lego’s manufacturing process, so the connection would be legal (some back of the napkin math suggests that to achieve this, you’d need a wall at least 20,000 studs long, so this or not practical, though for the sake of argument possible).
I would love to see a moc build with lots of angles in it where you use these techniques you've discovered so far, we would see just how much useful or not useful they are in a real build.
2:53 you can make second one legal if you use a 2x2 jumper rotate plate on top of it true 45° and don't add the 2 outside studs, so instead of being really attached, it's just held with tolerances. Lego does this all the time, it's the reason there are tiny gaps between bricks. Also you could just use rods. Like you could just put two vertical rods of any kind at 45°, slap a 11090 on each and put a rod in their holes
After the pythagorean triple video I spent a little time in Desmos and made a function that checked how close each 45 degree hypotenuse was to a multiple of 0.5 when the other sides were a multiple of 0.5 (thinking jumper plates could be used to provide more possibilities), found that having sides with a length of 14.5 was really close (20.50609 diagonal) and there were a few bigger numbers that were a little closer but probably too large to be practical, unfortunately I didn't have any lego handy to test how well it would fit, so cool to see a video really going in depth about this
the way i would deal with irrational lengths is to use those lego technic axel pieces that slide through blocks. a sliding rod is generally how lego seems to do it too. i recently built the new millenium falcon, and there was a ton of rods and hinges to get all manner of weird angles
I’m in the middle of a frustrating octagonal build - a model of the LEGO store at Dreamworld (because I’d already virtually built the Dreamworld entrance in Studio. And like Edna Mode; “well I just couldn’t stop darling!” This requires all the walls to connect to each other using a complicated mix of hing plates, 2L bars, 3L round plates and 1x1x2/3 bricks as the corners have columns made up of 2x1x1,2/3 snot bricks faced with 2x2 33° double slopes to snugly fit the gap where the two walls join at 45°, which means the column is half that to each of these walls - 22.5°. But of course the whole wall has to float on 6 sides with connection to the building’s floor on just two opposite walls. It’s all a virtual build in Studio atm.
9:15 Putting the 1x1 square clip bases in between studs at an angle like that feels a bit illegal, though if you put 1x1 round underneath it should be good
@@bricksculpt OH my mistake, I didn't realize you were putting them directly ON a stud, and that's providing the attachment friction! For some reason (I think because you said "in-between the studs" I thought they were being put like in the gaps between studs with the corners poking into the studs providing the attachment force.
The ultimate solution would be for Lego to make a range of parts with studs at sqrt(2) spacings. Wouldn't hold my breath waiting for that to happen, though.
Early on you ask if anyone else has done a 45 with a turntable. I built a tree out of the diagonal panels and wanted it at a 45 to the grid. The middle of the base connects to a turntable on the ground, surrounded by tile, with 1 more stud in just the right spot. I could tell that's about as far as I could get with that technique. You can place one small structure at a 45 with a turntable and lock it in place.
Luckily, things don't have to be perfect with LEGO. You just need to get within acceptable tolerances. If your sides are at a length of 8.5 or 12, the corresponding hypotenuses will be 12.021 and 16.971, respectively. Sounds close enough. At a side length of 20.5, the hypotenuse will be 28.991 - almost perfect. (You will of course need to use jumper plates for the .5 distances).
I'm currently building the BlueBrixx "Astronomers Mansion", and the designer implemented a couple of hinge-based 45° angles. Quite astonishing how far you can deviate from the perfect length before it feels wrong. 5/5/7.071 and 17/17/24.042 triangles felt like normal connections, and only one of the 7/7/9.900s felt a bit strained - which might even be a cumulative (negative) tolerance effect resulting from the fact that the hinges are high above ground, each sitting on top of a pile of inverted slopes. Still, 0.1 deviation sounds like a lot and I'd probably refrain from using that in my own MOCs. 0.07 should be OK when using "softer" bricks like LEGO, GoBricks or Qunlong.
You should now be able to build a 16-sided obelisk, even if you only anchor half of the walls... ...north/south/east/west already align to the LEGO grid... ... this video shows several ways to anchor the 4 walls which are at a 45°-angle... ...the resulting 8 securely-anchored walls can then be the anchor points for the remaining 8 walls... ...OR... ...the 8 anchored walls can be spread apart far enough to support a PAIR of walls, between each pair of anchored walls, so that your obelisk can be 24-sided!
Your "sugar grid" has a scientific name, specically from crystal theory: Coincident Site Lattice (or CSL). It's a nice little rabbit hole to dive into if you wish.
I have, and every time you called them sugar grids, I swear I wasn't shouting "They're CSLs" at my phone lol. In fact they also have a standardised notation in which they are identified with numbers. Here's a timestamp to a video that explains it quite well: th-cam.com/video/SqJTVT5FO9I/w-d-xo.htmlsi=VWzHygf3q52uFsov&t=4m40s
I have always found 45 degree angles. Ot too did using some of the thing you showed the issue is adapting the corners of the pate that is 45 degrees back to 90 degrees on the edge without it looking bad on the outside. You should cover that.
I think, don't get too hung up on connecting everything in both ends every time. I think perhaps what people have meant by using hinges or turn tables is that one such connection allows you to get any angle, including 45 degrees, and then just limiting the freedom of motion at the other end is enough. Perhaps similarly to the last technique shown in this video. If you are building walls at an angle, by finding "close enough" sizes you can make it work really well by just leaving the non-perfect fit at the ends. There is a 0.1mm gap between bricks in the system anyway, so if that gap at the corner is just a tiny bit larger it will be virtually unnoticeable. For example, the Jazz Club uses a 7x7 section placed at a 45 degree angle (on just a 2x2 jumper in the middle) in a space that is 10 studs wide. Since the diagonal of a 7x7 is 9.899... it's close enough that you don't really notice the gaps. Of course, you can't legally connect the corners with hinge plates for example, but you don't need to, you just need to make sure the 7x7 section isn't free to rotate. It can then be secured at the top in a similar way, in the Jazz Club build they use a 4x4 turn table (on jumpers) there. Another useful size is 12x12 with a diagonal of 16.971... close enough to 17. If it's slightly smaller than a whole number, it is always legal. But even if it's larger, it should still be legal as long as it's within the 0.1mm tolerance, which is 0.0125 studs. That being said, there aren't many more useful size examples until you get really large builds. Covering the ends of walls with simple SNOT techniques, like adding a tile on its side, should open up many more possibilities of getting "close enough" like this.
I love the math here. So I’ve got a challenge for you. Conquer these curves: Ellipse Oblong spheroid (football) Equilateral hyperbola Catenary curve (Gateway Arch) Bachistachrone curve Marilyn Monroe
My initial thought was a turntable surrounded by tiles. Build off of the turntable and then have posts from the base grid coming up to limit the rotation. Don't have any LEGO convenient so I can't make a build to see how hard it'd be to find good post locations (though, the posts could maybe be a stud rather than a brick or plate, so maybe it'd be easier than I think)
Bravo!! :D The technique u show at 13:00 or so is very sleek! When you talked of it saying "2 degrees of freedom" I was like "Yeah that sounds like Bebop baby!" I was thinking, about some ways the pieces connect... When did it all start? The Brick has...decades. No way they ops They were thinking of this when conceiving Lego. This is an expression of thought. But WHEN in the Lego history has been implemented? Already with the first 1/3rd height bricks?...
i feel like with that moving foundation method you could make a realistic building that resists earthquake damage by shifting slightly to absorb the vibrations xD
Jumping off of angles, I'd love to see a video talking about curves. Specifically, how to make curves that attach to the grid in multiple places while also allowing for the placement of walls of different length segments, like 1x4 segments, 1x6 segments, etc.
I found a legal snug 45 deg using the round pieces, the corners are open so the studs have room to move while still connecting perfectly. Looks like I can’t upload pictures, but you can probably mess around with one and figure it out, I had to offsett the walls with a jumper
Given √2 is irrational, there's gotta be some large multiple such that if you make a right triangle of LEGO bricks with that length, then the diagonal between them would be close enough to an integer that it would be within the tolerance of a legal LEGO connection!
I love that in today's world where ADHD 10 second shorts/reels/clips/whatever rule the internet, I can still find these kind of videos where someone goes into autistic detail in a super niche aspect of an obscure topic. As long as we have this kind of strive for betterment and ingenuity, I feel that humanity will be okay.
The next hurdle will (always) be; how do the corners of the 45 degree wall and the in-grid 90 degree wall match up with each other, without having awkward gaps or ridges.
You are correct that will be a hurdle. Need to find ways to blend them together and each technique gives it a different position relative to the standard grid.
As I've been playing with my new tubing bender lately, I can tell you that .2° off is "Just good enough". And I know you can feel my discomfort admitting this. :D
@jessetroller-yx8zd No, unfortunately I struggle to insert videomaking into my caleidoscopic list of interests, so, no BV building channel, _YET_ :D (The build project's name would be differnt tho).
@jessetroller-yx8zd My brain stopped picking up maths after a^2 +2ab + b^2. Joke, I can't even recall what was the thing before that, the compressed polynomia. LOL. I got back some grip on maths when a professor constantly connected it with geometry on the xy plane. I love geometry, my recent brainrot is suspensions geometry. It's esoteric, such a fascinating brainwreck. I really struggle to abstract beyond that, it should be why I feel no good at pure maths. ...There's a video (maybe Veritasium) about how ancients conceived numbers. Like they weren't "abstracting", even irrational numbers were a very tangible thing for them. Where we se a sqrt 2 they saw the diagonal of a square. Pitagora's theorem was probably born staring and counting rectangular tiles while meditating in a thermae's pool or a sauna, they say. Mindblowing. Feel jealous.
Is the corner garage not a 45 degree angle? I'm only asking because I know they use hinges and round bricks to achieve the angle. I guess you've made me curious now. I'm really loving these part and lego math videos lately. 🔥 👍
They use a similar technique to this, where they just build a wall on top of a plate that’s only connected to a single 1x1 round tile among the flat tiles around it, and put it on a 45. They build it so that the ends of the wall connect to the 90 degree walls with 1x2 round plates, which are skewed ever so slightly due to the irrational angle but do strengthen the wall. See the speed build & pay close attention to the part where they build the bottom “foundation.” Not even sure if it’s legal to connect the round plates like that as the 2 studs it’s spanning are not the same distance as 2 studs side by side. Classic LEGO breaking its own rules.
what about 60 degrees? i like heaxagons, and i know that it can be with hinges. (example catan moc) but i like a 6 length sided but also fill it completly... wich options are there ? (so not only the border, but also fill it completly with studs, tiles and or bricks ? (i'm also a wargammer :) )
This is definitely off topic, but as someone who livestreams build sessions, I’ve been wondering about your setup. Mine uses a Logitech camera, mounted sort of overhead and it drives me crazy; especially when the builds start getting too tall to keep in frame. I love that your framing is the builder’s perspective, which is what I would like to change over to, but I worry that a tripod will be an obstacle between the table and me as I build. Would you be willing to show and talk about your setup?
Yeah lol it sucks. I film on a chair basically straddling a tripod, and it's hard to reach or see what I'm working on. I have an extension that is on the way where you can have the tripod off to the side and they the camera come over in front of you. We will see how that goes.
@@bricksculpt Ah thank you for clearing it up and good to know. I thought the sharp corners of 1x1 tiles would be considered illegal. Have a great day and thank you for all the educational content you post.
Technically you can have a 45° angle anywhere easily. It will just have to have only one stud connection. Edit: or put the centre of a plate on a turntable and you could spin it to 45. But again, not a strong connection.
Taking your last few videos together, I think you're within sight of the ULTIMATE GOAL... (_insert "drumroll.wav" sound file here_) ...an "OCTAGONAL OBELISK"!!!?! ----- My only question is, how close to the apex do you want to continue tapering it, before you "cap" it with a "Sauron Eye of Flame", using battery powered light bricks? Because that would dictate the scale of the model, & thus the level of detail. The sides could be as smooth as the Washington Monument (to demonstrate proof of concept), or as rough as in the "Lord o.t. Rings" (to help conceal the residual hairline gaps), or anything in-between. 😂
I don’t think your double turn table/ double 2x2 jumper plates are exactly 45 degrees. Since they both pivot on one connection point they are probably pivoted at slightly different angles meaning they aren’t lined up perfectly on the 45 degree angle
th-cam.com/video/wdPGGpGcR0M/w-d-xo.html Here is my 3D sugar cube made of headlight bricks I promised. Stud and anti stud. Not sure what you would do with it but...
Absolutely fabulous video. Snot sugar grids is on my to do list. I haven't experimented much with them but I think it has a place and now I'm thinking it's quite possible.
Like on a wall? No reason it can't if you use for example a ton of stacked 1x2x5 bricks with 4 studs on the side. That makes use of the fact that a 2x2 plate sideways is the same height as 5 plates.
Why is it so important to be able to make a 45 degree angle? If you want to get more freedom from the square grid, and have things be more freely layout, then 45 degrees is about the worst angle you can choose. It is still very "griddy".
Depends on the application. If you are lining up buildings or making castle walls 45 would be very helpful. In a nature setting or thong randomly placed aboit at angles then I would agree.
Nice work! Sadly, I have stopped buying any Lego as the sets are so bad in quality and so expensive for no reason at all - 😩💩🤮👎. Fortunately, Funwhole & Panlos (to name but two) are fantastic alternatives: better quality at a fraction of the Danish billionaires' prices - 😊👍👌❤!
As a mathematician this is really heartwarming video to me. This is math! This whole video is just fun with math!
Thanks! I know it's making me enjoy math quite a bit without having to really study equations but rather trial and error practical connections.
Best LEGO content on the internet. Anyone can review sets. This is true learning and teaching. Keep it up!!
Thanks, that means a lot to me!
stages of grief with sqrt(2):
- blissful ignorance
- annoyence
- deep hate and giving up
- finding that it actually can be done, if you're creative enough
- joy, pride, love sqrt(2)
Lol love this
what a world it would be where sqrt(2) was rational
According to the Manhattan taxicab metric, the diagonal of a 1x1 right-angled triangle is perfectly rational.
Yes!
I’m searching for the joke but can’t find it. Help
@@mitchhak2 it should be 2 if I'm not wrong since in Taxicab distance, a metric invented for Minecraft purposes, moving one on diagonal means having to move 1 on X and 1 on Y, there are no diagonals in Minecraft. Manhattan, I was for saying "Mahanttan", my bad.
Loving to see my inputs (maybe others said it tho) come back across the new contents!
@@mitchhak2NYC cab drivers drive off the road and through buildings to take shortest distance.
The Jazz Club set has a section at 45deg. It uses 4558957 on a 4517986. That is built up to provide 2 studs that connect to the regular grid (the building wall at a separatable level) via two long tile pieces. See page 109-113.
Yes I have seen that. Thanks for mentioning that.
My eyes went big when I saw what you were doing with your adjustable angle technique. I stopped what I was doing, and it was amazing. And yes, please show an example of this technique on a Mils build. I’d like to see something of a semi-finished 32x32 section that would show off the true 45 of a building interacting with another building perhaps, or a fence etc. maybe a corner tower that’s at 45? Whatever you might come up with, your curiosity is a breath of fresh air, and I thank you.
Thanks! I need to put that in a mills plate for sure
1:33 finally proof that √2 is rational
Love this, especially the clips-with-bars technique. You do skip over some of the more simple ways Lego uses. 1: The angle plate (cursed piece #1) works fine if you just need a short-ish wall. It does have 4 studs, so is quite strong, AND the side lines up perfectly with a 45° wedge plate. 2: You can put something on a single stud (with hole) or a turntable and just limit its movement. Café Corner is the set I remember pioneering this. Corner Garage uses a technique similar to the one you show with rounded 2x1 plates, but not in parallel, which restrict the movement, and fills the gaps with 1x1 double slopes (which have a 45°-ish angle). The Botanicals use quite a few techniques to attach one or two stud-wide parts at 45°. One strong variant I can think of: using technic 45° angle connectors combined with bricks (1x1 or 1x2) with axle holes on both sides.
For a challenge: Fill a half-brick gap (So one brick on the grid, the other on jumpers) between two bricks perfectly. The only way I currently know (I think, I haven't done the math) is very clunky and requires a gap with a height of 4 studs. A Technic 1x2 half-width lift-arm works for a height of two studs, but is a pain to attach and you can see the rounded edges.
Thank you for this video first of all!
Some math here: 15:20 The distance between the corners of the dark bley tiles is mathematically slightly below 10 studs, 9.9 or more precise SQRT(98). But tiles are slightly rounded, so this works out. With the round plates at opposite ends of the white structure there is even more room than legally needed. The distance between the centers of the round plates is 15 studs, this is the same as the hypothenuse of a 45deg triangle with rectangular side of about 10.6. This is slightly nor than the required 10.5.
I also want to mention a building technique I have once used, but which is quite complicated. Using 45deg technical connectors #4 (part 32192). One could build some framework with axles and technic brick with axle holes where two exactly 45deg grids could be connected. Due to the possibility of sliding axles a little bit this is possible.
Thank you! I don't dabble in technic much but as you mention technic could definitely add some 45 degree angles. For some reason I always favor figuring it out with plate and bricks lol.
12:55 If anyone notices that your walls move a bit, you could use the excuse that it's to make the building earthquake-resistant.
Lol I like that
Wow those are some excellent techniques! Thanks for sharing! Sqrt(2) has vexed me as a builder since as far back as I can remember. So it’s awesome to see you take it on! One of my fave techniques for getting 45 degree walls is the technique used to build the front wall of the flame yellowish-orange museum portion of ninjago city gardens. It’s achieved by attaching a row of piece 35464 with vertical snot connections along the two sides of the wall in question, then locking the assembly into the structure with modified rail plates, I recommend checking it out if you’ve never seen it before, it’s pretty clever!
I will check that out. Tomorrow's video is a new technique I dreamed up last night for 45 degree angles. You must watch it it is perfect!
I'm not a builder but I enjoy your videos, and as a programmer I can see the sweat and tears into making the impossible work ☺
Big kudos for you imagination and dedication!
Thank you so much. I'm glad you enjoy them!
I love these videos that go in depth into the whole LEGO angles thing lol
Thanks!
Attach a turntable to a 2 x 2 plate with pinhole (part 2817), and you can slide the plate along an axle. A few of these assemblies will get you any angle you want.
Excellent video, Chris! Building on your 45 degree wall idea with your clips and bars, you can use a 1x2 or a 1x2x5 brick with the vertical groove in the center, and finish off, change directions at the ends of your 45 degree wall. I hope I said that so you will understand my idea.
I love that clip technique!
Oh the old garage door track piece! I like that idea thanks.
The last one is really amazing.
Thank you
I think one of the videos you should make next would talk about the 1/4th plate. Since the length of 1 stud is 2.5 plates, and brackets are .5 plates, there are times where we can get .25 plates like with a jumper or a clip in the middle of a brick. They’re kind of annoying to work with but it could be important to point them out. I needed to deal with them a lot in one of my recent MOCs
I like the idea let me see what I can do.
The only part I know of with a natural connection that creates a 1/4 plate gap is 4081a (NOT the modern one 4081b) this thinner ring is exactly 1/4 plates thick, though clunky to use in a build
@ yes I’ve noticed that too. It also reminds me that the half lift arm has it aswell because it’s half of 2.5 = 1.25 which is helpful and annoying in some cases.
It's actually possible to build at 1/8th the thickness of a plate and even smaller. But it is not easy and I am not good at it. Luca Hermann is a master of it.
@ that is incredible. Smaller than that seems impossible but really cool and I’d love to see how to use it.
Numbers of the form n+m\sqrt{2}, with n and m integers, are dense in the real line, which means one can find integer multiples of \sqrt{2} arbitrarily close to their nearest integer. Practically, this means if you had a sufficiently large enough wall, the turntable approach would work provided the wall is long enough that the error between the length of the diagonal and its nearest integer is within the tolerances of Lego’s manufacturing process, so the connection would be legal (some back of the napkin math suggests that to achieve this, you’d need a wall at least 20,000 studs long, so this or not practical, though for the sake of argument possible).
Love those 1x2 rounded pantographs!
I would love to see a moc build with lots of angles in it where you use these techniques you've discovered so far, we would see just how much useful or not useful they are in a real build.
I have been thinking that myself. What should I build?
@@bricksculpt the one world trade center comes to mind
Maybe an old western town if you are into that theme?
That clips-and-bar-at-45-degrees technique looks both simple and very useful, thanks!
Thank you.
I really love and enjoy your videos about this subject. Please continue with doing that! That is so good research you are doing. ❤
Thank you so much I will keep them coming!
2:53 you can make second one legal if you use a 2x2 jumper rotate plate on top of it true 45° and don't add the 2 outside studs, so instead of being really attached, it's just held with tolerances. Lego does this all the time, it's the reason there are tiny gaps between bricks.
Also you could just use rods. Like you could just put two vertical rods of any kind at 45°, slap a 11090 on each and put a rod in their holes
After the pythagorean triple video I spent a little time in Desmos and made a function that checked how close each 45 degree hypotenuse was to a multiple of 0.5 when the other sides were a multiple of 0.5 (thinking jumper plates could be used to provide more possibilities), found that having sides with a length of 14.5 was really close (20.50609 diagonal) and there were a few bigger numbers that were a little closer but probably too large to be practical, unfortunately I didn't have any lego handy to test how well it would fit, so cool to see a video really going in depth about this
I love your channel.
Thank you so much!
This was excellent. I love the detail you get into with these.
Thank you so much!
Always blowing my mind with these kind of videos!!
Mission accomplished!
This was very helpful for my moc I'm currently building. Thanks a lot, you got another subscriber.
You are welcome thanks for watching
I know some of the other comments mentioned it but just to express more interest, I would love to see some applications of these techniques.
Stay tuned!
the way i would deal with irrational lengths is to use those lego technic axel pieces that slide through blocks. a sliding rod is generally how lego seems to do it too. i recently built the new millenium falcon, and there was a ton of rods and hinges to get all manner of weird angles
That’s a great point and a very common technique for achieving these angles!
I’m in the middle of a frustrating octagonal build - a model of the LEGO store at Dreamworld (because I’d already virtually built the Dreamworld entrance in Studio. And like Edna Mode; “well I just couldn’t stop darling!”
This requires all the walls to connect to each other using a complicated mix of hing plates, 2L bars, 3L round plates and 1x1x2/3 bricks as the corners have columns made up of 2x1x1,2/3 snot bricks faced with 2x2 33° double slopes to snugly fit the gap where the two walls join at 45°, which means the column is half that to each of these walls - 22.5°.
But of course the whole wall has to float on 6 sides with connection to the building’s floor on just two opposite walls.
It’s all a virtual build in Studio atm.
Put it up on the discord server if you are looking for advice. There are so.e fantastic problem solvers on there. Sounds like a cool build!
9:15 Putting the 1x1 square clip bases in between studs at an angle like that feels a bit illegal, though if you put 1x1 round underneath it should be good
I don't see how it would be illegal. They don't touch. Lego does essentially the same thing on the roof of the Rivendell set.
@@bricksculpt OH my mistake, I didn't realize you were putting them directly ON a stud, and that's providing the attachment friction! For some reason (I think because you said "in-between the studs" I thought they were being put like in the gaps between studs with the corners poking into the studs providing the attachment force.
Beautiful video, thanks!
Glad you enjoyed it! Thank you
The ultimate solution would be for Lego to make a range of parts with studs at sqrt(2) spacings. Wouldn't hold my breath waiting for that to happen, though.
That would be interesting to see. I would wonder how the would integrate with other pieces.
Early on you ask if anyone else has done a 45 with a turntable. I built a tree out of the diagonal panels and wanted it at a 45 to the grid. The middle of the base connects to a turntable on the ground, surrounded by tile, with 1 more stud in just the right spot. I could tell that's about as far as I could get with that technique. You can place one small structure at a 45 with a turntable and lock it in place.
Yeah turntables are quite limited with the grid.
Luckily, things don't have to be perfect with LEGO. You just need to get within acceptable tolerances.
If your sides are at a length of 8.5 or 12, the corresponding hypotenuses will be 12.021 and 16.971, respectively. Sounds close enough.
At a side length of 20.5, the hypotenuse will be 28.991 - almost perfect.
(You will of course need to use jumper plates for the .5 distances).
I'm currently building the BlueBrixx "Astronomers Mansion", and the designer implemented a couple of hinge-based 45° angles.
Quite astonishing how far you can deviate from the perfect length before it feels wrong.
5/5/7.071 and 17/17/24.042 triangles felt like normal connections, and only one of the 7/7/9.900s felt a bit strained - which might even be a cumulative (negative) tolerance effect resulting from the fact that the hinges are high above ground, each sitting on top of a pile of inverted slopes.
Still, 0.1 deviation sounds like a lot and I'd probably refrain from using that in my own MOCs.
0.07 should be OK when using "softer" bricks like LEGO, GoBricks or Qunlong.
You keep blowing my mind I'm ludicrous frequency
Lol I'm glad you like the videos thanks
love your vids man
Thank you!
You should now be able to build a 16-sided obelisk, even if you only anchor half of the walls...
...north/south/east/west already align to the LEGO grid...
... this video shows several ways to anchor the 4 walls which are at a 45°-angle...
...the resulting 8 securely-anchored walls can then be the anchor points for the remaining 8 walls...
...OR...
...the 8 anchored walls can be spread apart far enough to support a PAIR of walls, between each pair of anchored walls, so that your obelisk can be 24-sided!
I have played around with 6 sided and 8 sided and the tip of my pencil is 16 sided but that's a lot of work lol.
Your "sugar grid" has a scientific name, specically from crystal theory: Coincident Site Lattice (or CSL).
It's a nice little rabbit hole to dive into if you wish.
Have you seen my videos about them? I dove quite deep and yes it is fascinating
I have, and every time you called them sugar grids, I swear I wasn't shouting "They're CSLs" at my phone lol.
In fact they also have a standardised notation in which they are identified with numbers.
Here's a timestamp to a video that explains it quite well:
th-cam.com/video/SqJTVT5FO9I/w-d-xo.htmlsi=VWzHygf3q52uFsov&t=4m40s
That is a great video. I still want to use my slang terms because it just rolls off the tongue lol
Thank you 😊
You are welcome
I have always found 45 degree angles. Ot too did using some of the thing you showed the issue is adapting the corners of the pate that is 45 degrees back to 90 degrees on the edge without it looking bad on the outside. You should cover that.
A turntable with only one stud ontop, finicky but extremely versatile
Yeah that would do it also.
How about using a 2x2 turntable with a 1x2 jumper and a 1x2 tile to create one? I can imagine some good uses for it.
I think, don't get too hung up on connecting everything in both ends every time. I think perhaps what people have meant by using hinges or turn tables is that one such connection allows you to get any angle, including 45 degrees, and then just limiting the freedom of motion at the other end is enough. Perhaps similarly to the last technique shown in this video.
If you are building walls at an angle, by finding "close enough" sizes you can make it work really well by just leaving the non-perfect fit at the ends. There is a 0.1mm gap between bricks in the system anyway, so if that gap at the corner is just a tiny bit larger it will be virtually unnoticeable. For example, the Jazz Club uses a 7x7 section placed at a 45 degree angle (on just a 2x2 jumper in the middle) in a space that is 10 studs wide. Since the diagonal of a 7x7 is 9.899... it's close enough that you don't really notice the gaps. Of course, you can't legally connect the corners with hinge plates for example, but you don't need to, you just need to make sure the 7x7 section isn't free to rotate. It can then be secured at the top in a similar way, in the Jazz Club build they use a 4x4 turn table (on jumpers) there.
Another useful size is 12x12 with a diagonal of 16.971... close enough to 17. If it's slightly smaller than a whole number, it is always legal. But even if it's larger, it should still be legal as long as it's within the 0.1mm tolerance, which is 0.0125 studs. That being said, there aren't many more useful size examples until you get really large builds. Covering the ends of walls with simple SNOT techniques, like adding a tile on its side, should open up many more possibilities of getting "close enough" like this.
The bar and click approach is really clever! I’ve never thought of it before
Thanks!
I love the math here. So I’ve got a challenge for you. Conquer these curves:
Ellipse
Oblong spheroid (football)
Equilateral hyperbola
Catenary curve (Gateway Arch)
Bachistachrone curve
Marilyn Monroe
Yikes that's a lot of curves!!!
Too simple. Not even a challenge really.
I wasn't sure if 9:16 was legal (placing a 1x1 plate at 45 degrees), but it's ~5.515 mm and there's 5.6mm space, so it checks out
Check out the roof on the Lego Rivendell set #10316. The whole roof Is covered like that.
My initial thought was a turntable surrounded by tiles. Build off of the turntable and then have posts from the base grid coming up to limit the rotation. Don't have any LEGO convenient so I can't make a build to see how hard it'd be to find good post locations (though, the posts could maybe be a stud rather than a brick or plate, so maybe it'd be easier than I think)
Yeah that would work.
Angles in application: intricate roof gables are my greatest enemy.
Bravo!! :D
The technique u show at 13:00 or so is very sleek! When you talked of it saying "2 degrees of freedom" I was like "Yeah that sounds like Bebop baby!"
I was thinking, about some ways the pieces connect... When did it all start? The Brick has...decades. No way they ops They were thinking of this when conceiving Lego. This is an expression of thought. But WHEN in the Lego history has been implemented? Already with the first 1/3rd height bricks?...
Thank you so much I'm looking forward to pushing that technique further and see where it goes. It was quite popular.
i feel like with that moving foundation method you could make a realistic building that resists earthquake damage by shifting slightly to absorb the vibrations xD
Yeah maybe lol solving the world's problems with LEGO
Please make a video about the full 45° building!
Such a cool technique with the 1x2 rounds
I'll see what I can do
Jumping off of angles, I'd love to see a video talking about curves. Specifically, how to make curves that attach to the grid in multiple places while also allowing for the placement of walls of different length segments, like 1x4 segments, 1x6 segments, etc.
I think that could be a good video, will have to try it out thanks.
I found a legal snug 45 deg using the round pieces, the corners are open so the studs have room to move while still connecting perfectly. Looks like I can’t upload pictures, but you can probably mess around with one and figure it out, I had to offsett the walls with a jumper
This is the imgur ID which, so if you look at any picture there you can just replace the id with this: 0m78CaY
Finally managed to post the picture Id: 0m78CaY
Also, it’s on imgur
Given √2 is irrational, there's gotta be some large multiple such that if you make a right triangle of LEGO bricks with that length, then the diagonal between them would be close enough to an integer that it would be within the tolerance of a legal LEGO connection!
Yeah probably. But it I'd probably too large to be used much in lego building.
I'd like to see something that uses these techniques. Like a little for example building.
I will see what I can do.
I love that in today's world where ADHD 10 second shorts/reels/clips/whatever rule the internet, I can still find these kind of videos where someone goes into autistic detail in a super niche aspect of an obscure topic. As long as we have this kind of strive for betterment and ingenuity, I feel that humanity will be okay.
Thank you so much. I know my approach is old fashioned but this is how I enjoy watching TH-cam so I'm glad others agree.
You should try and build a fire lookout tower, I have never seen a good one made out of lego and I think it could be an interesting challenge
I'll add it to my list
The next hurdle will (always) be; how do the corners of the 45 degree wall and the in-grid 90 degree wall match up with each other, without having awkward gaps or ridges.
Cheese slopes might help with that.
You are correct that will be a hurdle. Need to find ways to blend them together and each technique gives it a different position relative to the standard grid.
13:16
Yes Please! 😁
The only Always Legal diagonal is in 3/4 ratio, cause it's precisely 5. But the angles are irregular.
That is not correct there are infinite legal angles
There has to be a piece where the bottom connection point allows for a "sliding" connection. Im thinking something like those transparent 1x2 bricks
Lol watch today's video!
At least Technic and Mindstorms builders have much worse nightmares.
I believe it
As I've been playing with my new tubing bender lately, I can tell you that .2° off is "Just good enough". And I know you can feel my discomfort admitting this. :D
For a second, I thought you were CallanLoF.
@jessetroller-yx8zd No, unfortunately I struggle to insert videomaking into my caleidoscopic list of interests, so, no BV building channel, _YET_ :D
(The build project's name would be differnt tho).
1:30 yes this is illegal. Because no one can force Lego plates to do anything they don't want.
Lol
where can I get that mat?
It's from Rebrickable but they don't have them right now.
lego just needs to make a plate piece with the studs angled at 45 degrees.
Yes they do
"oh no, maths!!" XD
😁 always more maths!
TIME FOR EVERYONE'S FAVORITE SUBJECT, MATH! ANSWER THE THREE QUESTIONS CORRECTLY, AND YOU MIGHT GET SOMETHING SPECIAL! PROBLEM ONE...
@jessetroller-yx8zd My brain stopped picking up maths after a^2 +2ab + b^2. Joke, I can't even recall what was the thing before that, the compressed polynomia. LOL.
I got back some grip on maths when a professor constantly connected it with geometry on the xy plane.
I love geometry, my recent brainrot is suspensions geometry. It's esoteric, such a fascinating brainwreck.
I really struggle to abstract beyond that, it should be why I feel no good at pure maths.
...There's a video (maybe Veritasium) about how ancients conceived numbers. Like they weren't "abstracting", even irrational numbers were a very tangible thing for them. Where we se a sqrt 2 they saw the diagonal of a square.
Pitagora's theorem was probably born staring and counting rectangular tiles while meditating in a thermae's pool or a sauna, they say.
Mindblowing. Feel jealous.
Fun fact, the FBI investigates all illegal build techniques.
Felony
Brick
Interactions
It's true
It's true
Is the corner garage not a 45 degree angle? I'm only asking because I know they use hinges and round bricks to achieve the angle. I guess you've made me curious now. I'm really loving these part and lego math videos lately. 🔥 👍
Not sure I would have to look m at it. Thanks! I'm glad you like them.
They use a similar technique to this, where they just build a wall on top of a plate that’s only connected to a single 1x1 round tile among the flat tiles around it, and put it on a 45. They build it so that the ends of the wall connect to the 90 degree walls with 1x2 round plates, which are skewed ever so slightly due to the irrational angle but do strengthen the wall. See the speed build & pay close attention to the part where they build the bottom “foundation.” Not even sure if it’s legal to connect the round plates like that as the 2 studs it’s spanning are not the same distance as 2 studs side by side. Classic LEGO breaking its own rules.
@mitchhak2 I have the set myself, that's what made me think of it while watching. Very very interesting
Do you think it is illegal?
what about 60 degrees? i like heaxagons, and i know that it can be with hinges. (example catan moc) but i like a 6 length sided but also fill it completly... wich options are there ? (so not only the border, but also fill it completly with studs, tiles and or bricks ? (i'm also a wargammer :) )
Here's a video I did about hexagons a while ago.th-cam.com/video/_wOSUn5p67s/w-d-xo.html
@bricksculpt yes i saw that video.. but is only to go up.. what i like to see is how to conect is sideways to make a map of some kind ?
Closest to 45° angle I got was on the X-Wing mashup set
That's because TIE fighter wings use this mechanic
The problem isn't attaching a 45° wall, it's closing the gaps around it.
Yes that's a good point
I wonder if the lower tolerances of the lesser brands would allow for fudging these angles better.
Never thought of that.
This is definitely off topic, but as someone who livestreams build sessions, I’ve been wondering about your setup. Mine uses a Logitech camera, mounted sort of overhead and it drives me crazy; especially when the builds start getting too tall to keep in frame. I love that your framing is the builder’s perspective, which is what I would like to change over to, but I worry that a tripod will be an obstacle between the table and me as I build. Would you be willing to show and talk about your setup?
Yeah lol it sucks. I film on a chair basically straddling a tripod, and it's hard to reach or see what I'm working on. I have an extension that is on the way where you can have the tripod off to the side and they the camera come over in front of you. We will see how that goes.
@ what kind of camera are you using? DSLR? Higher quality webcam?
Phone lol
Hmm, would having a variant of 35480 that's 2.414U long fix this?
That's an interesting thought. I'm not sure how that would change things better or worse.
Take the wall at 45 degrees and add cheese slopes to angle it at 45 degrees. Pyramid incoming lol
That could be fun
I have to ask because I just dont know the answer: isnt it illegal to put the 1x1 clips between the studs like you did?
No it's legal. Che k out the Lego Rivendell set. They use the same technique on the roof.
@@bricksculpt Ah thank you for clearing it up and good to know. I thought the sharp corners of 1x1 tiles would be considered illegal. Have a great day and thank you for all the educational content you post.
You are welcome!
Technically you can have a 45° angle anywhere easily. It will just have to have only one stud connection.
Edit: or put the centre of a plate on a turntable and you could spin it to 45. But again, not a strong connection.
That's a good point
🤯
who knew it was so easy
Taking your last few videos together, I think you're within sight of the ULTIMATE GOAL...
(_insert "drumroll.wav" sound file here_)
...an "OCTAGONAL OBELISK"!!!?!
-----
My only question is, how close to the apex do you want to continue tapering it, before you "cap" it with a "Sauron Eye of Flame", using battery powered light bricks?
Because that would dictate the scale of the model, & thus the level of detail.
The sides could be as smooth as the Washington Monument (to demonstrate proof of concept), or as rough as in the "Lord o.t. Rings" (to help conceal the residual hairline gaps), or anything in-between.
😂
I could handle an octagonal one the ultimate goal would be tapered cylinder which I have experimented with and oh boy its difficult
Sauron would be cool!
I don’t think your double turn table/ double 2x2 jumper plates are exactly 45 degrees. Since they both pivot on one connection point they are probably pivoted at slightly different angles meaning they aren’t lined up perfectly on the 45 degree angle
th-cam.com/video/wdPGGpGcR0M/w-d-xo.html Here is my 3D sugar cube made of headlight bricks I promised. Stud and anti stud. Not sure what you would do with it but...
Absolutely fabulous video. Snot sugar grids is on my to do list. I haven't experimented much with them but I think it has a place and now I'm thinking it's quite possible.
Couldn't you use a 1x2 jumper? The stud has a lot more freedom to move around inside
Yes you could
Lego Minecraft heads are about sqrt2 studs long
45°-45°-90° rule 1:1: ²√2
Now do √ 5
Yuck
Still wondering if the sugar grid can be assembled using SNOT bricks…
Like on a wall? No reason it can't if you use for example a ton of stacked 1x2x5 bricks with 4 studs on the side. That makes use of the fact that a 2x2 plate sideways is the same height as 5 plates.
I'm going to work on that soon. Thanks for the idea.
Why is it so important to be able to make a 45 degree angle? If you want to get more freedom from the square grid, and have things be more freely layout, then 45 degrees is about the worst angle you can choose. It is still very "griddy".
Depends on the application. If you are lining up buildings or making castle walls 45 would be very helpful. In a nature setting or thong randomly placed aboit at angles then I would agree.
Brute force it with lots of 4211613 and 32028.
Nice work! Sadly, I have stopped buying any Lego as the sets are so bad in quality and so expensive for no reason at all - 😩💩🤮👎. Fortunately, Funwhole & Panlos (to name but two) are fantastic alternatives: better quality at a fraction of the Danish billionaires' prices - 😊👍👌❤!
I've heard good things about those alternatives but never brached out. Also Funwhole??? Who thought that name up lol.
Why art thou irrational
Stop being so irrational! 😁