This Technique Will Blow Your Mind. Unlocking The Secrets Of The LEGO Grid.

[@reddblackjack]

At first I thought it was brilliant. But it's NOT brilliant. It's revolutionary! I love it!

[@jonpgale]

I see what you did there 😂

[@bricksculpt]

Thanks bud!

[@TheRealMTH96]

Let me blow your mind even more. The 10297 Boutique hotel set uses this patern to set half of the building on an angle. Crazy part is the floors, I wound suggest looking into the instructions. Basicly two "random" wedge plates (54383 and 54384) put next to each other make a perfect filler piece for the gab between both grids.

[@bricksculpt]

Im going to have to look into that thanks!

[@StarScapesOG]

This is correct! That's a fascinating set!

[@mrmuffins951]

This is awesome! I was just wondering if there’s a set that uses this!

[@teakew8217]

10315 Tranquil Garden also uses this off-angle technique to place the shrine in the garden.

[@jossdeiboss]

Oh wow! Just checked the instructions and yes, it blows my mind!

[@Greenicegod]

A 45° angle would indeed be illegal, for the same reason Pythagoras was so upset by it. The length between diagonal studs is √2 times the horizontal length between studs. √2 is an irrational number, which can only ever approximate a whole number of studs over some distance. Some of those approximate distances would be within Lego's manufacturing tolerances, but you would never be able to construct a repeating grid without a defined origin point, like you can with rational triangles.

[@MissSmoozie]

Doing the math it's ~1.0% off. Grid is sqrt(24.5) and the 2x6 is obviously 5 long between the studs. This should be safe enough and shouldn't damage your lego.

[@alanschwarz]

Echoing the above, the reason the squares at 11:00 are 37 and 53 degrees is because those are the angles of a 3-4-5 triangle - which from your (awesome) prior video we know are 4-5-6 studs. I didn’t comment on that video, but the reason it’s 4-5-6 in LEGO instead of the legendary Pythagorean 3-4-5 is because the first stud is actually 0 - the “origin” (0,0) in math-speak. So the fourth stud is actually X=3. So in figuring out all these angles - particularly in this video - always consider the first stud zero and you can follow regular trigonometry. Yes, I was a math teacher! 💪💪💪

[@bricksculpt]

Well said Thanks for adding this!

[@clopec]

Immediately when I heard the angles a bell started ringing in my head, and I needed to look up the angles of Pythagorean triplets. Would only have needed to scroll down for the comments! Essentially you could think of these as two overlaid Lego surfaces, with one rotated 37 degrees. Then the studs that are common for both planes are marked with the green one-by-one round plates. You could also do an offset using any one-studded jumper plates, for instance replacing the one-by-one greens with tiles and the tiles with two-by-two jumpers.

[@Skeeve-Magick]

See it this way: The gaps between the studs give the (pythagorean) distance. So yes, The first stud then is Zero.

[@over2408]

Shouldn't other patterns be possible then like with the 5 12 13 triangle? And all the other whole number triangles?

[@adamclarkson]

I knew it was going to be 37° before he said it and I have no idea how i knew that lol! Some recess in my brain I guess lol😅

[@ramakho]

This is a game changer for city builders who want to get off the Lego baseplate grid. We need to see some city updates since you’ve been hinting to it in your videos.

[@bricksculpt]

Yeah I might have bog city news real soon stay tuned!

[@pinkraven4402]

Wow, normally I treat these tricks as interesting gimmicks, but this diagonal grid could be actually so useful for arranging buildings o_o

[@bricksculpt]

I agree completely very useful to me.

[@Mysda_]

This is the minecraft sugar cane pattern. Magical.

[@etheraelespeon1986]

And the Stardew Valley basic sprinkler pattern! When im building with it in either game, i envision it like moving a knight in chess and it helps a lot

[@janwip]

Came here to comment this, glad someone else noticed it too!

[@Alexjanchapro1]

I wonder if there's some sort of mathematical explanation for this pattern, like how the golden ratio pops up everywhere.

[@incarnate3276]

@@Alexjanchapro1there is: the triangle has a 90 degree angle, so Pythagoras gives us 5^2 = a^2 + b^2 because it is six studs long, but the attachment is made in the middle of the stud of course, so we got to calculate that as 5. I was confused at first when the math didn’t work with the six, until I realised that. It can be formed by two smaller triangles, which are a^2 = 2^2 + 1^2 ‎ = 5 and b^2 = 4^2 + 2^2 ‎ = 20 respectively, so it does indeed work because 5+20=25.

[@Tha_Seagull]

Hi Mysda! yeah it's really that.

[@PlutoniumBoss]

I recently put together the Christmas Tree (set 40573) and it uses exactly this technique to offset the tiers as you build upward. It uses sections of 2x2 cylinder up the middle, and each tier around these sections has a 2x2 gap in the middle. Then around this gap you put four studs, and then the next tier above you skew at an angle on those studs. All those different angles make for an amazing tree.

[@bricksculpt]

Nice I didn't know they used this I will have to check it out.

[@bricksculpt]

Nice I didn't know they used this I will have to check it out.

[@Oliver-wr5po]

​@@bricksculptWhy twice?

[@marcsfat]

@@Oliver-wr5po KZbin does that sometimes.

[@vindi167]

​@Oliver-wr5po glitch, happens to me sometimes too

[@Endigo_Vandane]

I'm just happy you understood what I was trying to explain. The beauty of a channel like yours is the fact that different techniques and discoveries can be shared among builders. I hope that giving this method some attention will allow it to be used in all sorts of new and exciting ways.

[@bricksculpt]

Yes I agree! Thanks again for the tip!

[@zwitshr]

The extra effort put into actually making the explanations aesthetically pleasing is so worth it

[@bricksculpt]

Thank you!

[@dfordnut]

Thank you so much! I spent last night trying to attach a building at an angle unsuccessfully came down this morning to your video. I am going to try this method. I am a trial and error Lego person too.

[@bricksculpt]

Perfect timing lol

[@eyedeerman]

9:34 he adds the accidently missing round stud on the bottom right of the top half of the plate at this moment if anyone was wondering 😎

[@bricksculpt]

You caught me

[@calvinroberson4655]

@@bricksculpt as soon as you brought the pattern out it was the first thing I noticed and I was like NOOOOOOOOOOOOOOOOOOO

[@svendsmitha.623]

You can think of the movement of the knight in chess for the grid placement 2up1left instead of placing and removing all the plates for windmill pattern

[@Stevo_1985]

The tolerances of Lego has always impressed me. It's little wonder it's lasted so long. Properly engineered.

[@bricksculpt]

Yes I totally agree

[@VioletSaathoff]

6:30 it's definitely illegal. It "works" cause 3.5√2 ~= 4.9497, which is close enough to 5 to be within tolerance. Another option which should work slightly better would be 7-stud spacing hitting the corners of a 5x5 square (5√2 ~= 7.017, which is very close to 7 - this has about 1/4 the error the 3.5 stud solution has)

[@VioletSaathoff]

14:27 for similar reasons as earlier, I don't think this is legal either, but I haven't actually checked this - that being said, this is all still really cool!!!

[@VioletSaathoff]

Also, 45deg will never be possible with a system like this because √2 is irrational. I.e., there is no pair of integers (a, b) where you can write a√2 = b

[@lucahermann3040]

1:55 they do make 5 wide. There's a 5x5 macaroni plate which also allows this technique.

[@bricksculpt]

Yeah as usual you are right :P

[@walkerbrowning3642]

For anyone wondering, the 20x20 square is actually off by 2.6% of a stud from being exactly 20 which when divided across the whole length is only a 0.14% error or 11 microns per stud. This is likely well within LEGO’s own manufacturing tolerances. As for the fitting of plates between studs the gap is about 2% smaller than it should be to accommodate the plates based on a 12:20 stud:brick width ratio so this technique is likely (technically) illegal

[@digitalrandomart3049]

whats cool is that you will be able to stack these angles on top of eachother. lets say you are doing a landscape you can use this to angle a part of the MOC and then angle something else on top of that

[@bricksculpt]

Yeah that would work well!

[@TonyBolger-w7r]

The Christmas Tree set (40573) uses this in stacked form to generate various branch angles around a circular trunk

[@ArcherJLady]

The grid at 7:40 is also the exact optimal water source grid for growing sugar cane in minecraft! In minecraft, in order for sugar cane to grow, the ground it sits on must be adjacent to at least one water source, so by placing water where the black studs are, all the sugarcane (grey studs) are then adjacent to exactly 1 water (black studs), and every water is adjacent to 4 sugarcane, allowing for the highest sugarcane to water ratio! Now, I have no idea how relevant this really is, but I don't know maybe the math between why this patern is optimal is similar in both scenarios. Edit: Dark green, not black lol

[@Reegeed]

In case of sugar cane you have perfect tiling of a cross shaped tiles. In lego can be tiled that way bcs of hidden pytagorean triple. And all triples are tilable.

[@bricksculpt]

Good to know lol I don't play and probably will never play minecraft but good to know anyway :P

[@poopemoji8874]

This was exactly the same thought I had

[@Roger_808]

thats exactly what i was thinking lol. i recogized the patern immediately

[@pikminfreak0011]

It's also the optimal pattern for basic sprinkler placement in Stardew Valley. They water the crops directly adjacent to them, so they need the same spacing.

[@tremkl]

Your comment about a village is great. You could use this technique to make a village much more organic, and if you did the pattern in greens, you could disguise it as lawn for the houses. Would give you the freedom to have the houses not all be at right angles with each other.

[@bricksculpt]

Yeah it would be cool to see this on a big scale in a moc.

[@terdragontra8900]

You can do this with any diagonal square grid (other than a 45 degree grid which doesn’t do anything special), so there are technically infinitely many legal angles. Though you have less and less attachment points as you choose larger grids, so this one is the most convenient.

[@bricksculpt]

Yes, that is correct. The appeal to this one specifically is the amount of attachment points.

[@nicholauscrawford7903]

What do you mean by "legal" in this context? I'm only casually interested in Legos, and I don't see why we would outlaw any of this.

[@AnttiAlajuuma]

@@nicholauscrawford7903 Building techniques that are called "illegal" are those that cause extra stress on pieces. Sometimes for example two studs at an angle are close enough to lego grid that you can force a piece in to connect to both but if the distance isn't exactly correct, it will try to stretch on compress the pieces.

[@Not-THAT-ChrisPratt]

You, sir, are the Einstein of Lego! Not only do you come up with this kind of thing, but you present it to the rest of us to use. Thank you.

[@bricksculpt]

Wow, thank you so much for your support!

[@ToshibaAirConditioning-RAS]

Lego geometry is always so satisfying and beautiful.

[@bricksculpt]

I agree!

[@nellam8]

9:33-9:34 bottom right ... sneaky fix

[@bricksculpt]

🤣🤣🤣🤣 I'm so glad someone saw that!!!!

[@MarcoServetto]

you should make a simple town square in mini scale with a circular fountain in the center and buildings circularly all around

[@bricksculpt]

I like it!

[@Ponk_80]

It was great seeing the moment where you discovered something new that you had not thought of before. I love this feeling when I play around with creative software, where I discover fun things that I didn’t know was possible to do, before I discovered it. It’s such a great feeling.

[@bricksculpt]

I agree it's very satisfying to figure out something like this on your own, even if it's been done before.

[@M0torsagmannen]

this is really cool, thanks for showing your findings in such a clear and informative way

[@bricksculpt]

Thanks! I'm glad you enjoyed it.

[@vokhev]

I've used this before to angle buildings and scenery. It's nice to have fences at an angle.

[@bricksculpt]

Oh yeah that would make a sweet fence angle

[@maple22moose44]

1x2 jumpers in a stair step pattern between the studs would also work and make an even more complete grid

[@Ponk_80]

Yeah I just sat down with some grid paper after watching the video, trying to see how many patterns that I could come up with, the 1x2 jumper plate is a valuable piece.

[@bricksculpt]

I will have to experiment with that!

[@christianheisch8472]

This is great. It expands my pythagoras pattern, that I used for several architecural models by more studs. Thank you for sharing.

[@bricksculpt]

You're very welcome!

[@franimal86]

This is so fun. I’d say the 2x6 brick has 10 unique angles then, not 6. I love that you pointed out why they were tan. I was like “did he really run out of grey??” haha The last 2 grey angles match the last 2 green angles working backwards, so they are duplicates, as you said. But then, there are 4 green plates that would continue the angles all the way until you turn the block 90 degrees. If you include the 45 degree angle, that is 10 unique angles for a 2x6 brick. Now I wonder how many angles you can get with longer bricks! There must be a mathematical proof made of this asap.

[@jossdeiboss]

This came out at the perfect time! I am planning to build some houses on a hilly area, and was trying to figure out how to put the buildings at an angle, with enough strength and without pivoting parts. Amazing!

[@bricksculpt]

Awesome, let me know how it works, sounds like a cool build.

[@jossdeiboss]

@@bricksculpt I will! It's probably my first attempt to build something more complicated, so I have no idea on the results, but I'll see what I can do and let you know :D

[@TheUkuleleTim]

10:25 that protractor looks ridiculously useful, definitely not the worst!

[@bricksculpt]

It's just got a lot of wiggle room in it.

[@Skoozi]

The grid of studs you laid out appear to be the movement pattern of chess knights!

[@bricksculpt]

Indeed they are

[@schubie02]

This is a very interesting video. I was waiting for you to angle another square of 2x6 plates on top of your brown examples, in almost a spiral fashion.

[@bricksculpt]

Stay tuned new video will cover that.

[@Arthur.N.L]

I noticed that you can place the grid in diagonal lines so that you don't have to use 2x2 plates. Or you could use the hop of a knight from chess. I hope that this was helpful.😁

[@bricksdarklighter5597]

By far the most useful LEGO content on youtube. Thanks for doing an amazing job with these videos!

[@bricksculpt]

Wow, thank you so much!!!

[@madgorila8]

To keep it short, incredible and very helpful. Thank you!

[@bricksculpt]

Thank you so much!

[@Panic_Pickle]

if you pick an "L" shape (two steps and turn right OR two steps and turn left) it's easy enough to do without the filler squares. Can go from any point, take two steps in any direction and turn your chosen corner and place a spot. Filler does give stability though so that's nice.

[@landsgevaer]

There are even more options, like fitting the corner studs of a 6x6 plate on the corner studs of a 2x8 plate (because 5²+5² = 7²+1²), and that will make two different possible angles actually.

[@lucyg00se]

Hehe yes came to say this, when I saw the video title I initially thought it was gonna be about sum-of-two-squares-in-two-different-ways grid angles

[@IronVicero]

The pattern of the studs reminds me of the same pattern used in Minecraft water source placement, for growing sugarcane with maximum efficiency. In the game, sugarcane will only grow on a block that is directly to the side of a water source, not diagonally from one. So for maximum efficiency of the land used we place water sources in this pattern, resulting in every available space that isn't water viable for sugarcane growth with no gaps, maximising the viable placement of the sugarcane plant To map the pattern easily, you can start with one stud or watersource anywhere, then place more around it as though it was a knight from chess moving around a board, one side/two advance or two side/one advance.

[@adamgoss3638]

That's mind-bending! If it really doesn't stress the plates and bricks, it could make for nonstandard placement of structures in a MOC. A woodland or wilderness cottage leaps to mind, a place you'd expect a house to be built without confirming to a city grid pattern. (of course you can build houses in rl on a plot of land any way you want to, but this is Lego where everything follows a grid plan - usually!)

[@bricksculpt]

That would be a super cool build!

[@samday6621]

I remember it as placing (horizontally) 1 every 5. Next line up, move two spaces left/right, 1 every 5. This will be great for building a Japanese garden with a winding path of stepping stones.

[@bubby6858]

Congratulations. You found the hidden secrets of the system. Its so precisely made. That all kinds of stuff is possible. And its been that way since the the 60s (i think)

[@bricksculpt]

Well said!

[@stephaniemcdonald4132]

Game changer, outside of the box thinking. Can we get this guy working for LEGO already?! Yeah their LEGO show master builders are great, but we need someone like this innovating legal building technics that are outside the box.

[@bricksculpt]

Wow thank you so very much for your kind words!

[@manoelguidialvares6903]

Can't wait to see the continuation of this video! Seeing how you'll apply this technique to s building!

[@bricksculpt]

I have two other videos out about this check then out!

[@brucelucas1756]

I have to thank you for such an informative video. I've been wanting to build a city grid that wasn't just flowing in the usual patterns and seeing this has made me want to explore the possibilities of different offshoot roads, like the real world.

[@bricksculpt]

Thank you. I'm glad you found it useful!

[@dustinzaccaria7644]

You share a lot of useful information. I be learnt so much from your channel. This technique is by far the best trick I’ve learned from your channel and that’s a very high bar to meet. Kudos on the great video. Thank you.

[@bricksculpt]

Wow thank you so much for all your support and compliments.

[@joshuasims5421]

6:17 3 and a half studs over in both directions will fit a 6-stud plate, but it is illegal: square root of 3.5^2+3.5^2 is 4.94, almost the distance of five between the first and last stud of the 6 plate. However, it’s so close I don’t know if it would hurt the pieces. 2.5 studs over in both directions will have a length of 3.53 studs, just a little past the length to fit a half-stud from the end of a 5 plate. Also a little illegal but I think either should be safe to achieve that coveted 45 degree angle for builds. I do think the other angles are completely legal, especially the ones that rely on Pythagorean triangles. So cool!

[@NatShulamoo]

i saw this same technique in the bonsai tree set to angle the tree, the botanical siries just has the most insane legal techniques, the cool thing is that they used one of those rotaty parts so that you can have more connections in between the gaps

[@LegoSauc3]

I’m now shopping for a protractor. Angle work makes everything look so much more real. Thanks great vid!!!

[@bricksculpt]

Nice! Thanks so much

[@infinidominion]

Opens up a lot of creative architecture options

[@natef15]

I'm watching this during lunch at work and when I get home I'm implementing it immediately. Great video!

[@bricksculpt]

Thank you so much!

[@nathanielaustin7268]

Would love a follow up about wedge plates that may interact with this! Is there a wedge plate angle that will blend the two angles? Or maybe some SNOT slopes?

[@victrrrxxx1533]

can our cursed pieces fit in here? xd

[@erikgiroday257]

If you put a 2x3 (or 3x6) wedge on the normal grid its mirror will line up on the rotated grid. This is utilized in the Boutique Hotel set for getting the furniture aligned with the angled wall

[@bricksculpt]

Probably lol

[@bricksculpt]

I will have to try that

[@dragonshadow1902]

I am using a technique similar to this for my off-road course. I have a 1 : 45 rc 4x4 jeep. So, to make an incline, that also turned 90 degrees. The only difference is that instead of the 1x1 round plates, I used the 2x2 plates that swivel. This allowed me to rotate any angle that matched up but also have better support underneith my 2x8 plates.

[@G7ennx]

I always enjoy using a 3,4,5 triangle. Try placing a single square 3 to the right an 4 up from another and you can place a 1x6 straight (five steps) between them. Thanks Pythagoras!

[@bricksculpt]

kzbin.info/www/bejne/eIbWoIp6mruMidU just did a video on that a few days ago

[@smap0]

I also discovered this about a year ago when looking at some ways to connect stuff diagonally. I used for one building in my lego city because i wanted it at an angle. Nice video i still learnt a lot xD

[@bricksculpt]

Thanks! It's definitely not new but under talked about!

[@greenmat6855]

Bricksie wants to add an angled road to his city. Someone needs to inform him of this magic.

[@bricksculpt]

Send if to him lol

[@Pystro]

6:20 At first I thought that's the 12-12-17 quasi-pythagorean triple, which is off by 0.17% (or very very close to 1 in 577). But it's actually the 3.5-3.5-5 or 7-7-10 quasi-pythagorean triple. It's off by 1.01% (or very very close to 1 in 99). At 14:15 that's the 18-6-19 quasi-pythagorean triple. It's off by 0.14% (or very very close to 1 in (18^2+6^2+19^2) which equals 1 in 721). They are actually 19 apart (despite the fact that you're measuring it with pieces that total 20 studs in length).

[@bricksculpt]

Yeah I said it wrong thanks

[@Pystro]

You'll probably wonder if these are legal. I'm certain that that depends on the length over which you stretch these. Something that's off by 0.17% over 17 studs is off by 2.89% of a stud, and after 34 studs it's off by 5.78% of a stud, which is already worse than the 3.5-3.5-5 triple, and so on. A way around this would be to leave (hopefully imperceptible) gaps between parts of the building. This will always work for quasi-pytharoean triples where the diagonal is slightly too long (and thus wants to pull on the pieces on the diagonal) - although the gaps might grow to perceptible size for larger discrepancies. And It _might_ work for when the diagonal is only ever so slightly too short (and thus wants to compress the pieces on the diagonal). The diagonal is: too long for the 7-7-10 triple, too short for the related 5-5-7 triple, too long for the 12-12-17 triple, too short for the related 17-17-24 triple, and too long for the 18-6-19 triple.

[@rarewhiteape]

9:27 the open studs allow for half-stud offset on 1-wide bricks and plates too, don’t forget!

[@dottedboxguy]

ooooo that's very interesting geometry ! i'm 100% sure there's an arithmetic proof to say that putting the bars in between the studs is legal. one thing that you've probably noticed is that theoretically, you only need 3 of the green things to hold a bar in place, 2 at each end of the bar on the same side, and one in the middle of it on the other side, technically all you need to hold the bar in place, it's probably impractical though. note that the bar's slope is 1/3 or -3/1 , as in they'll plot like y = x/3 and y = -3x on a graph there's probably something quite similar for the plates, but it's not as obvious just looking at it you may also notice that to build the stud pattern, all the green studs on a line are a fixed number of studs apart (5 here) and between lines they get offset by a fixed amount of studs to the left or to the right (2 here), according to which way the pinwheel tiling is rotating. by messing with these constants, you might end up with other interesting tilings that aren't especially square looking ! there's definitely a lot to explore here for sure, and it can all be represented with a bunch of modulos and proven that it's legal with a bunch of arithmetics which i really dislike personally

[@bricksculpt]

A few people have said they think that part is illegal but it doesn't seem to fit too tight.

[@joshmonroe7166]

There is an angled plate in 72° and it lines up perfectly with the 1x plates between the studs. That could potentially close up some gaps really nicely.

[@gotztago]

There's a lot of wonderful math here. In higher level math, the grids you're talking about are called integer lattices, and they can be thought of as being constructed by an orthogonal (right angle) basis of integer vectors. Say the basis vector is (a,b), like (2,1) or (2,3), etc. You can measure the angle as theta. What's really interesting here is that by doing the flip, you are basically rotating the grid by 2theta--as an example, that's why 45 degrees gives you a full 90 degree rotation! But if you take the vector (a,b) and rotate it by the angle of (a,b), something interesting happens--this is best calculated using complex numbers, but the vector you get is (a^2-b^2,2ab)/(a^2+b^2), and has a length equal to a^2+b^2, which is always going to be a rational number. The end result: you end up finding a Pythagorean triple in your grid, with a hypotenuse of length a^2+b^2, and edges of length a^2-b^2 and 2ab. As an example: (1,2) gives you a the (3,4,5) triangle, as you can see! And the (1,4) case gives (15,8,17).

[@bricksculpt]

That's a great breakdown, thanks!

[@stockicide]

Technically, they did make 5-wide plates: Part 711 "Plate, Modified 5 x 6 with Hole." But the piece was retired in 1974 and only used in 22 sets.

[@Reeuwijk78]

The LEGO christmas tree uses this principle. It makes for interesting rotation angles of the branches. I also made it two stories higher with the remaining parts using the same priciple.

[@bricksculpt]

I have been told this and I need to check it out!

[@dsjove]

This too is using pythagorean triplets. The square edge are fastened 5 lengths apart. If you. were two draw straight lines you will get you 3 and 4 when they intersect. You should build some of your previous strangles onto this grid; the 90 decrees point will be on grid, but without a stud.

[@bricksculpt]

Yes I will try that soon!

[@seanfine3463]

Crucial information that unlocks infinite new possibilities.

[@bricksculpt]

I agree!

[@m2pt5]

You can create a 45 degree angle with a 4x4 round on top of a turntable, supported (at the gaps in the round) by four 1x1 rounds, each between 4 studs. Edit: A 1x1 round between 4 studs is not illegal, they use it in official sets.

[@bricksculpt]

I wasn't calling it illegal I was calling the length likely illegal.

[@DefinedBy]

@@bricksculpt You're right in your assumptions; that this length is illegal, and that a 45 made in this way will always be illegal. The distance between the stud and jumper space you describe is 3.5 * root(2) = 4.95 (approx) versus your 2x8's studs' distance of 5. I don't know the thresholds for good fits, but it's neat that 5% of a unit is acceptable for a clean fit. If you were to take a 2x14 plate, and space 11 between the studs, it should fit even nicer than the example you showed. There aren't many marginal errors in practical lengths (ie less than 20 or so), so it's neat that you found a usable one. Great video (as always), and thanks for giving inspiration. I can't wait to try out these techniques in my own builds!

[@noptimized]

You can use the 3 x 4 x 5 triangle to attach 1x6 plates to a grid along these diagonals: o o o o o o o o o o o o o o o *O* o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o *O* o o o *O* o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o *O* o o o o o o o o o o o o o o o o Put studs or 1x1 blocks where the bold *O's* are, and then you can "log cabin" 1x6 plates on it. I just worked this out from watching your video! EDIT: Aaaaand, I just realized that you did a prior video demonstrating this. If anyone hasn't seen it, go watch that one too!

[@bricksculpt]

Lol I was going to say did you see my previous video. Thanks for all the input!

[@christianbrix4311]

Another fascinating video, and I don't even build Lego! Would love to see some more of your creations as well at some point. You keep showing us these great little staircases, water fountains, showers, armchairs, treadmills etc, but it would awesome to see some of your city

[@bricksculpt]

Yeah my city is a mess right now I've really been focusing on the technique stuff. I will do something soon but it will have a twist.

[@mrnicomedes]

At first I was thinking: diophantine equations, with some slop, perhaps. Turns out, nope. Not at all :D I continue to love the fact that "doing lego" ... "legally" has rules. Thanks for sharing the creativity and joy that exploring within constraints allows for! I now feel like "theoretical" and "applied" lego should be their own disciplines.

[@bricksculpt]

Glad you enjoy it!

[@Smona]

after a bit of calculation and experimentation I found out two things: 1: the angles for that 1×20 strategy are 71.56505118° and 18.43494882° which is not very helpful if you're trying to achieve specific angles and they have to be precise. 2: you can get many different angles though, if you stack multiple layers of the grids and/or the 1×20 strat. some examples include: 53°, 37°, 71.565°, 18.435° (these are obvious, just one or two layers), 16°, 74°, 90°(very complicated way to turn 90° when you can get the same result by just putting some plates or bricks down) 34.565°, 55.435°, 69° (nice), 21°, 32°, 58°, 85°, 5°... since 5° (with five layers of stud grid) and also degrees ending in every single digit are possible, theoretically, with enough studs, enough large plates and enough space from the floor to whatever you wanna build, any amount of degrees without a decimal point are possible, anything from 1° to 90°. Is this practical? no. Is it fun to know? idk dependy on the person. I did notice that unless you wanna use the 1×20 slide to get unreasonable angles, using grids that are rotated in different directions is not useful at all, since they just cancel each other out. so unless you want 55.435° or 34.565° using both types of grids above one another doesn't make any sense. But if you want any normal angles, just multiply 37 or 53 by some number (which is the amount of same grids) and subtract a multiple of 90 to get the angle

[@Smona]

TL;DR: if you don't care if your baseplate is a meter (or for the americans: 39 inches and three eighths) thick, you can get any angle that you can write without a decimal point

[@bricksculpt]

I didn't think to stack them to change angle that genious!

[@paulharris4256]

The two plate set-ups you’re describing around the 10 minute mark are mirror images. If you held a mirror vertically between the two and look in from one side you’d see the other shape. (Hope this makes sense? Like your left and right hands, identical, but different)

[@bricksculpt]

Yes absolutely makes sense. That's a good way of describing it thanks!

[@JD2jr.]

Two things. 1: you should be able to get more angles if you use the 2x1 "jumper" plates, so instead of only being able to move 1 stud closer up/down or left/right, you can move over a half (similar to using the circles in the middle, but you'd only go 1 direction and not both. and 2: use this strategy multiple times to get other angles. so... 37degrees, 74, 111,148, 185... I'm sure there's some overlap but there are a ton of options.

[@bricksculpt]

Watch the newer video it has more details about different angles.

[@bensbrokenbones4102]

This could be used to give so much character to terrain and landscape around the build

[@bricksculpt]

I agree I want to make a diagonal river with it covering the edges with angled plates.

[@robbiedobbles]

You sir are a god among men. You have inspired so much creativity these last few months

[@bricksculpt]

Wow! Thank you so much you are too kind.

[@AnmAtAnm]

Cool that the 18.5⁰ is exactly half of the 37⁰. Should be able to make a nearly perfect 19-sided polygon (usually 71.1⁰ interior angles, instead of these 71.5⁰) with the two techniques. Or a gently curving wall.

[@HollywoodF1]

12x12 has a diagonal length that is less than 1/4 of a mm from 17, which is 5% of the diameter of a stud. That’s the best low-integer rational approximation of 45º.

[@quinnbalfour2139]

I don't say this often but this is fantastic!

[@bricksculpt]

Thank you :)

[@redabiel]

Incredibly interesting! Great watch

[@bricksculpt]

Glad you enjoyed it! Thanks

[@nickpatrie7668]

Wow! Of all the LEGO videos about cool or unique ways to build, this is the best one I’ve seen in a long time. I will definitely be trying this out.

[@bricksculpt]

Thank you so much I'm glad it was helpful!

[@nearG_Green]

Fun fact, that pattern of studs is also the same pattern used in Minecraft for sugarcane farms.

[@2.Plus.2.Equals.5]

You could use this to make circular structures. Think a piece of graph paper connecting points, you'll eventually get a curve going.

[@bricksculpt]

Yeah probably could

[@otoolec29]

would love to see a video investigating how the angles produced with these methods can be applied to create interesting mechanical movement with technic pieces!

[@bricksculpt]

Me too but technic is my weakness lol

[@aprcktiplaal9293]

its easier to use slope rather than angle for measuring these patterns the slope is just "height per distance" meaning if you raise by 1 stud after 2 studs of sideways (looking from top) you have a slope of 0.5 (1/2) or 50% (if youve ever seen road signs that show a hill going up or down and it says a percentage, thats how that works) and the angle is always the arctan (tan-1) of the slope (atelast it should be). meaning a slope of 1 (1/1 or any multiple of this) or 100%, it will be 45°

[@bricksculpt]

I like that idea, good to know thanks!

[@MetaHydra-gj6ms]

I tried this like 3 years ago and didn’t think anything of it lol. But now that I’m more advanced in building, maybe this technique will help me

[@phallicusoblongus]

I remember figuring this out at a basic level about 17 years ago when I was about 8 years old. I thought it was cool, but I had no idea what I could do with it. Didn't quite have the ability to connect the dots and figure out what solutions it provided. I was also only really thinking in the basic XYZ axes.

[@hanspetrov4343]

Who would have thought, the optimal way of growing sugar cane on minecraft, makes a very useful lego grid for city building

[@BenisJam]

This is absolutely genius! Love making these discoveries with you!

[@bricksculpt]

Thanks!

[@stijnvth]

They should make plates like this. Awesome.

[@bricksculpt]

Yes I agree

[@lennynash8221]

I really love your videos. You make the videos that I've always wanted to see, but Noone really made. I really enjoy your "parts we need" series. Keep up the good work 👍

[@bricksculpt]

Thank you so much for all your support!

[@johnydl]

a 1x6 should fit on a 4x5 diagonal perfectly, but that's the only reasonable pythagorean triple the next would be a 14 long plate on a 6x13 slant

[@justfellover]

I got your point upon glancing at the thumbnail, and it took 15 seconds of watching the video to confirm my initial guess correct. Well done, and well reported. Thank you.

[@bricksculpt]

You are welcome

[@Pystro]

At 9:40 -ish, you can put 2x2 jumper plates in places where the plates on top have their middles. (Or in other words, everywhere except where you'll have the edges of two plates on top meeting.) [edit: ah, you mention it at 12:16]

[@crayder1100]

"Complicated to set up..." Psh, I've made enough ultra efficient sugarcane farms in Minecraft to recognize the best placement pattern. This patter, where the pegs are, every empty space is touching exactly one peg. This is how you use the least water and make the most of any space to get the most sugarcane in any area in Minecraft.

[@dsjove]

I had never seen this technique before. Thank you.

[@bricksculpt]

You are welcome!

[@sneakyfred]

Incredible discovery. I'd played with the 2x6 corner rotation before, but never conceived of extending to arbitrary plates! Also I guess that 18.5 degrees is half of the earlier 37? Just a hunch, no proof (yet)

[@bricksculpt]

Thanks!

[@eugenetswong]

You all look like such geniuses! Well done!

[@bricksculpt]

Thank you! Lol

[@chrissjackson6488]

6:06 the spacing is ≈ 3.536 pegs.

[@commander-fox-q7573]

That’s very interesting. For the type of MOCs I make I can’t think of a direct use for this but it’s so interesting I’m definitely going to file it away just in case it ever comes up. It’ll definitely be very useful eventually. And I can think of so many cool uses for this in landscape type MOCs. Nice find and great explanations!

[@bricksculpt]

Thanks, yes I agree landscape mocs would be my go to use for this.