Why you can't make a Perfect Circle with Beacons in Minecraft

[@jeo1812]

0:43 "A baking tutorial for a cake you'll never bake" *Awkwardly turns to see my collection of recipe books*

[@quantumblur_3145]

You're not obligated to make every recipe in every cookbook

[@frandurrieu6477]

​@@quantumblur_3145 Heresy

[@Aerolite_FPS]

Wysi likes

[@duckexe_]

Osusosuusousosus​@@Aerolite_FPSwysi 727 wysi !!!!!

[@Monotone_Fallen]

No but same-

[@eshleyyy]

I actually like the fact that it looks very random from the outside, but when you stand on the center block it becomes a perfect circle. I really like chaotic designs like this and having them come together so beautifully is wonderful. I must build this in my hardcore world!

[@squibble111]

ill post the schematic of both the world and the armor stand tols in the schem channel in my discord, if you want to take it, or possibly make your own (if you have a bigger gradient)

[@kr1v]

@@squibble111 how would you get a bigger gradient? Isn't 5 glass blocks the max?

[@mystik_owl]

@@kr1vthere are FAR more permutations than just these 96

[@sebastiangrau8409]

@@kr1v you could switch between more colors. He didn't include the values or brown. You could also reuse colors in your gradient, or do something crazy with mixing 3 colors at once

[@eshleyyy]

@@squibble111 I was thinking of making a muuuuch bigger circle for one of the farms im cooking and I was already thinking id have to make the datapack from scratch, but ill gladly take and modify yours, thanks!

[@OrigamiMarie]

I have never watched your channel before, but I'm sold on "baking tutorial for a cake you'll never bake". The pair of rings thumbnail was pretty great too (though a rainbow beacon thumbnail would have done the trick quite well).

[@squibble111]

going rainbow beacon would have been a nice throwback to the first video, woulda looked cool. though im glad i went with this, youtube seems to like it

[@OrigamiMarie]

@@squibble111 it definitely creates the contrary assertion that brings in the clicks. But also, you deliver on it!

[@ChibiKagura]

​@@squibble111 yeah, i like that simple and technical thumbnail so it really got my attention

[@alexo_pog]

@@squibble111the thumbnail definitely pulled me in from the main page so i say its working

[@acookie7548]

i probab;y wouldnt have watched if it was just a tutorial onb how to do that. ig why i clicked is the why behind the given diagrams. good video

[@PCHSwS]

I love designs that look completely random from most perspectives until you stand in the right spot and suddenly it makes sense... I am contemplating trying to incorporate this into something I can build on our SMP now :D

[@Kaadjoisanavaliwithtoomuchtime]

its like those pictures made out of lots of hanging objects. they are so cool!

[@kipu44]

copy pasta 😜 accidental?

[@PCHSwS]

@@kipu44 oh my god, two people that have a similar opinion! How could that happen??? Drama!!

[@PCHSwS]

​@@Kaadjoisanavaliwithtoomuchtimeyou mean like Squibble's perspective art? :D kzbin.info/www/bejne/iIalmGdngLqmaKssi=pMjevp67jfdVtPc8

[@glompert7390]

@@kipu44OH MY GOD, PEOPLE HAVE THE SAME OPINION??? HOW WILD!!!

[@Frozen_Hope]

Gives the same vibe as those art pieces that are loads of bits on strings but forms a coherent picture when viewed at a specific angle

[@CraftyMasterman]

this blew my mind

[@LimolaGaming]

omg it's crafty

[@aspidinton]

blows up pancakes with mind

[@JasminUwU]

Dirt blocks have low explosion resistance, so that makes sense

[@squibble111]

omg its crafter counter

[@lucashu1247]

cop flop > crafty counter

[@daireks]

i assumed the problem was that you couldn't place beacons next to each other or something lmao 😭 so, when you explained that it was actually that the spacing was uneven i thought it was a bit silly. BUT!!! i also completely understand the fun in solving random small problems like this so i quite enjoyed watching haha

[@artyfarty99changingtohoiii78]

same 😅

[@painovoimaton]

Same here! Turns out it was a very neat perspective puzzle.

[@Dezloxe]

Looks considerably better from the inside than outside, maybe thats it.

[@kipu44]

Like the Tardis. 😁

[@MichaelPohoreski]

Title is partially clickbait. People assume, and rightly so, that a perfect circle refers to *world space* beacon placement when the author is talking about beacons in *screen space* (when looking up.)

[@widget5963]

@@MichaelPohoreski Yeah I was kinda expecting something like finding a best-fit radius for a 96-gon that's still fully loaded at once on a standard server. This was kinda neat anyway though.

[@milkflys]

you could probably consider how it'd look from the outside when deciding how much to space out the beacons and compromise a little bit on the size consistency without it mattering too much

[@wackid2370]

​@@MichaelPohoreskiwell yeah people should know that's impossible in a cube grid game

[@the_ant_guy]

It's like drawing an infinitely large 96-gon centered at (0,0), then drawing a line from the center to all 96 corners, then getting the minimum integer coordinates on that line outside a defined radius around (0,0)

[@HEHEHEIAMASUPAHSTARSAGA]

The integer coordinates can only approximately touch the lines, cause most of the lines have irrational slopes, which means they never exactly hit any grid points except (0, 0)

[@adnzip8198]

doesn't even have to be infinitely large, it can just be big enough that the beacons all fit inside. There's definitely a way to automate this

[@nddragoon]

@@HEHEHEIAMASUPAHSTARSAGA for 96ths of a circle i think a pretty decent portion if not most slopes are rational, still, you can just try to find the closest it gets to a block center within the specified radius

[@-minushyphen1two379]

@@HEHEHEIAMASUPAHSTARSAGAAlthough they do get arbitrarily close, if you go out far enough

[@HEHEHEIAMASUPAHSTARSAGA]

@@nddragoon I plugged the values into wolframalpha and it seems like all the slopes are irrational except the cardinal directions and diagonals (so 88 out of 96 are irrational). Though you can get arbitrarily close to any slope, it might require you to go out too far and make the beacon beam appear too small. It's an interesting question what the maximum allowed radius should be in order to make the effect look (subjectively) the best

[@SimplexonYt]

you actually found a solution for the problem im trying to solve since half a year

[@squibble111]

congratulations on being the single member of the uninentionally targeted audience

[@itripleo5780]

It can easily be done with some trig tho

[@sluggy1739]

@@itripleo5780nerd

[@drippylad3973]

​@@itripleo5780 Hush, mathematics graduate

[@RubiksCubeNerd3]

Do the trig and get us a graph of it ​@@itripleo5780

[@grungko]

i did a rainbow beacon in the past and wanted to make it a circle. It didn't look good due to the gaps between the beams as you explained, but i said it was acceptable since it was a single player world and no one would see this lol. I actually might reload this world and fix this rainbow beacon, to thank you for this video !

[@onebacon_]

NOOOO sqrt 2 stikes again... disgusting irrationals. we must embrace hexagons

[@Faroshkas]

Hexagons, embeded with sqrts(3) all over the place...

[@gallium-gonzollium]

@@Faroshkasb- but hexagons are the bestagons..

[@WindsorMason]

​@@gallium-gonzollium even the bestagons betray us

[@nartoomeon9378]

sqrt 5 : (sad)

[@dagurtheone3969]

@@nartoomeon9378golden ratio!! :3 pentagons :333

[@ai-spacedestructor]

so the conclusion is that warehouse style is the best approach to almost anything.

[@matchstick33]

I get the vibe that you have a passionate nerd rant (/pos) to go on about this, and I have never heard of this concept before and an so intrigued, care to explain? lmao

[@ai-spacedestructor]

@@matchstick33 not really a rant, its just i find there is a specific style of doing things i always fall back to and maybe thats because im a really ptractical person who doesnt do any decorative stuff, so it 100% only has the functionality it needs to and nothing else, which i tend to describe as "warehouse", "factory" or "industrial" style. there isnt really a big thing behind it, also even if there was. its so long ago that i saw this video that i would probably not remember what my thought was anyways.

[@DogBat]

3:24 that is actually gorgeous It looks like a star

[@CNSninja]

I feel like this kind of thing could almost be a numberphile video. This is a really cool lesson in perspective and why the idea of "perfection" is actually very subjective. Have you ever seen one of those sculptures that looks like a big chunk of nonsense, but shining a light on one side reveals that it casts a perfect shadow in the shape of a familiar object, and then shining a light at it from another angle casts a different shadow of a different familiar object? It's a fun way of playing with perspective. This video reminded me so much of that sort of thing. The way the circle looks careless and messy from almost any angle until you stand at the middle of the circle and it all organizes itself almost as if by magic, is genuinely an awesome thing to see play out. I love anything that can illustrate the extent to which perception can affected shape your ideas about "reality."

[@NitroLemons]

Absolutely agree. The subjectivity of perspective is a fascinating topic in general, and one that spans multiple fields of study

[@datengineer2174]

You know had you NOT pointed out the difference in spacing I might never have noticed but now its forever going to torture me. Thank god this video also handily fixes the issue you just pointed out.

[@akkiruksavage554]

So excited this video has inspired my next two weeks of Minecraft obsession. I made a bunch of farms for beacons as my last project and then kinda stopped playing a few months back. Now I know what to do with all those beacons

[@_wetmath_]

this is quite interesting. and it may be possible to calculate and assign a score to different possible beacon placements based on 1. how close the of the beacon block is to the ideal angle line, and 2. how wide the apparent beacon beam is relative to the other beacon beams this is worth investigating, I'll have a look into it myself

[@squibble111]

Ooh, that would be really cool to design a program to do that! if you do come up with sometihing please do let me know on the discord server

[@ClaraDeLemon]

Assigning scores would be a great solution instead of brute forcing! For closeness to the ideal line, it should decrease with distance, as differences in horizontal gaps would not be as noticeable at large distances I think. And for calculating apparent wideness vs other beams, you would need to know their sizes first to compare, which would make it recursive and weird. I think if you instead swap that for "distance to center", you would get the same effect, as beam width scales with radius! Really neat math problem overall, I wonder if there could be a formula that gives a more straight answer than just computing all the values and picking the best

[@JPK314]

​@@ClaraDeLemonThis leads to a diophantine equation which is unfortunately NP-hard to solve in general. However, optimization isn't too hard via a branch / prune approach, and with this particular problem you can find good bounds fairly easily that exclude all but a small number of possibilities that can be easily checked

[@ClaraDeLemon]

@@JPK314 It wouldn't be a diophantine equation, as the slopes of the straight lines are all irrational, and even then you dont want to find exact solutions, you want to find approximations, which is much easier to do than finding integer sols.

[@schwingedeshaehers]

​@@squibble111sry for the ping, but has someone come up with something? if not, i will try something, but first want to know, that it isn't solved yet

[@potaatobaked7013]

This is really cool! The method you used very much reminds me of ray marching, which is typically used in rendering. It would only take a small tweak to the ray marching algorithm to turn it into a tool that does this automatically.

[@squibble111]

Oh yeah absolutely. Something I could try is spawning a shulker on each site and since shulkers snap to blocks, I can easily find the closest point to the center of the shulker

[@tverdyznaqs]

I feel like there's a maths dessertation somewhere in there. Like you just sort of brute forced this problem with a rotating armor-stand but I bet if an actual mathematician took a crack at it they would probably be able to deduce some sort of formula that approximates a circle on a square grid in this specific way. That's what fascinates me about yall redstoneheads, sometimes you guys just end up doing incredible maths recreationally and I think there's something quite pure and wholesome about that :3

[@flamekid574]

An interesting problem and a genius solution. You explained it all really well, kept it interesting, and the result was awesome (the warehouse light effect was a really nice touch). Great video all round!

[@squibble111]

Thank you !

[@ЗинаидаЛеонова-ю5у]

What I learned instead is that no two men's OCD is the same

[@TheTrueMichael]

This was... Incredible. I'd love a block-by-block tutorial on how to build this exact setup (for those of us not savvy with commandblocks :)) and I already have a plan on where to include it, but I totally get if you want this to be a ”figure it out if you can, this was my project and i want it to stay that way” thing. This felt really cool and informative and for the first ever video I've watched from you, you gained another sub

[@squibble111]

Glad you enjoyed it! Theres a WDL for everything in the discord, and you can modify things to how you please. Theres also certain programs being used in the server so you could ask around if you want to use a computer to generate things instead.

[@michael23b]

That’s awesome. While it wouldn’t be perfect, I think it might also be cool to simply increase the “thickness” of the circle, to have more beacons at each turn covering the gaps. Edit: actually this is a stupid idea cause you’d still have the same visible gaps between some of them unless it was extremely thick

[@vulpesinculta3478]

Perhaps if it is layered thrice? Though maybe it would need more.

[@michael23b]

@@vulpesinculta3478 to efficiently cover the gaps even more I think he would just need to plot more points the same way he did, but at a smaller turning increment

[@rtrichter]

to increase the desnity you would have to increase the number of turns in the circle. Say you triple the number of turns, then you find 3 spots for each color (or you could have the colors repeat three times its up to the builder really). You would probably need a bigger radius to fit all of these beacons but I think this would increase the density better than making it thicker would.

[@martinshoosterman]

​@@rtrichterincreasing the number of turns would cause beacons to need to be placed even further to find ideal spots for them. While layering the beacons wouldn't have much variation in distance.

[@rtrichter]

@@martinshoosterman layering the beacons at the same rotations wouldn't have any effect. Additionally layering them would require more distance as well. You need to find a second point along that ray that is close to an integer coordinate. When you stand in the middle that coordinate will just be behind the first beam (and since its farther away it will be smaller and completely invisible from the center). Layering them at a higher frequency decreases the distance between beams and therefore "covering the gaps" which is what OPs intention sounds like.

[@partiallypeculiar4545]

You've made something incredibly epic here. I immediately recognized the Smile Rancher ruin music too so that's awesome as well

[@matth8617]

I really like this style of video where you build something useful or fun and explain it. Tbh I couldn’t care less about how quickly you could destroy a hoe but would watch so much content if you explaining things like this or like the anvil launcher that was one of your first videos. More practical mechanisms, redstone or not, are far more interesting to watch, at least for me

[@GlossyPigeon]

It’s an anamorphic piece of art really. You’ve overcome a technical limitation to create something circular in a square world.

[@adamhayes4691]

I always love seeing one of your videos come out. They’re always so unique to most other people’s. And you explain things so well. You’ve come a long way since before you even had one thousand subscribers, not that long ago, but you’re still just as entertaining, if not more

[@squibble111]

Thank you for the compliment. I appreciate you having been here since then, the channel's definitely come a long way

[@Autumn-Leafeon]

I really like how it looks like you could put in a natural path to travel to the inside/outside of the circle, too, which I really like.

[@kolamostic]

I saw the title of this video and expected some sort of "Wifies" explanation type thing, and I don't usually get interested in those types of videos, however, I was really interested in your video by the way you conveyed things. You and Gneiss Name could be a good, underrated Minecraft duo, you earned a new subscriber.

[@squibble111]

Thank you, im honored to be batched into the same group as the great gneiss name

[@Mirolp7]

i like your calmness, a lot of Minecraft content creators are so over exaggerating. But you Sir, you are just doing your thing and its interesting to watch

[@happysmilesworldandgames8755]

7:56 "but, *in the end* ..."

[@гксгк]

it doesn't even matter...

[@Whenpigfly666]

Gotta love how the perfect circle looks like a starting position for Conway's Game of Life.

[@Cooly-noob]

This is a very smart and accurate solution to the problem. I have already built a beacon circle before, but i haven't thought about this problem.

[@maxsam5498]

I’d recognize that music from anywhere It tickles my brain with nostalgia

[@seulseulgom]

the second u faced the camera upwards, i got it, i dont want no explanation, i dont understand why it happens but the fact that it works blows my mind and i wanna keep it that way, liked and subbed tho, great content!

[@Lawry-nwyfu]

Squiddy , this video has made me rethink my whole life , my wife came back , my son loves me again , my ex finally got over our breakup . Squirrel, there aren't words in the English language that can show my appreciation so I'ma just say - Thank you Pookiebear

[@kapsaysin]

This is something I’d likely never build, but is genuinely so cool that I can’t help but admire it.

[@wChris_]

the diagonal distance is sqrt(2), which is 41% bigger than beacons just next to each other. You can calculate the distance using Pythagoras' theorem.

[@MxMxffin]

yeah sure but this is not actually the angular difference. Both circles with diameter 34 and 35 can be built using 96 beacons. I'd go with 35 since i don't like double centers. you have 96 Blocks so your ideal Angular differences should be 360°/96 which is 3.75°. If you are in the middle of that circle and look south. The center of that block and the center of the block next to it have an angle of 3.37°, the next two enclose an angle of 3.34°, then 3.3° and then 3.23°, then when the first offset block comes the angle rises to 4.11°, 3.2°, 3.07°,4.44°,2.89°,4.57°,4.7°,4.76°, and then in reverse. The angles are all different.

[@Superwaffle-ez9ct]

loved this whole concept but WOW that redstone circuit at the end was so cool, i have to do that for a build some day

[@LimolaGaming]

You cant because it is a game with cubes.

[@fizipcfx]

i think he is aware that this game contains cubes

[@ShadowDancer1000]

NUH UH

[@costa-w3k]

You can because it's a sandbox game

[@dirtydan3029]

​@@costa-w3k i found no sandboxes in this sandbox game 0/10

[@The2024Not-Channel]

​@@dirtydan3029suspicious sand stores stuff like a box,10/10

[@SilicatYT]

Amazing video! Love how you explained how you came up with the shape

[@Grinthex]

You are right, I will probably never build this, but you made me want to and that sir is a success in my book.

[@ВіталікБритан-х7ч]

7:30 I can see binary counter here)

[@Kaiasky]

I really like the armor stand raycast. The resulting effect is really cool. I like the effect from places slightly off center, where they're not perfectly aligned but there's not an obvious grid pattern

[@slbubuzamazal5518]

Such a neat problem. Awesome video

[@epicrainbow]

i actually needed this for my server with some friends, thanks!

[@mirosVEVO]

Splendid choice of music :)

[@squibble111]

hi bronkulator

[@Shieldzany]

Isn’t the background music from 0:17 A certain area of slime rancher?

[@AureaTW]

YESS it's from the glass desert i think it's called that in English?

[@Shieldzany]

@@AureaTW thx

[@Shieldzany]

@@AureaTWwait no it’s where you unlock the ancient ruins

[@MooMania4]

Ancient gate is the bame

[@Shieldzany]

@@MooMania4 thx

[@AverageCentipedeHater]

The most unexpected song you can hear in a Minecraft video is a Slime Rancher theme to be honest

[@squibble111]

whats also surprising is the disproportionately large amount of rain world fans who watch my videos. i don't know where they all come from

[@bomblii]

omgg u have a little lantern hat :3

[@pedrom4572]

cooking tutorials for dishes ill never make are the only possible cooking tutorials for me

[@Drawoon]

nice to see I'm not the only one who figured out the right glass pattern for a good rainbow

[@santi-ago]

Dude u have made the PERFECT thumbnail 😧 i always keep clicking on this video no matter how many times i have seen it in my recommended. Good job

[@vulpesinculta3478]

Holy moly you are an absolute genius, love ur videos, they're always not only interesting, but explained in enough depth to make even a layman like me understand the concept!! :D

[@imoutofthisgame]

"Why you can't make a Perfect Circle with Beacons in Minecraft" 2:49 THATS LITERALLY A PERFECT CIRCLE WITH BEACONS IN MINECRAFT

[@clumsytav]

As Kendrick once said "A perfect circle's never perfect only filled with lies" Very deep conceptual lyrics.

[@thenameofxavier]

A baking tutorial for a cake you'll never bake is a fire line

[@genericalias2179]

this is so beautifully overengineered

[@percycreeper2733]

ah, yes, the slime rancher music :D

[@samstedman409]

God damn I hope you’re an engineer irl bc this is really smart. The second I saw how you used the armor stand I was like this guy is a genius.

[@Plaegu]

Mom: Your OCD isn’t that bad Me: … I need the beacon beams mathematically perfectly apart.

[@foxglove-woods]

the ingenuity here is incredible, seeing the problem and deciding there must be a way to solve it instead of decrying it as a 'quirk of minecraft' is incredible

[@Qeuy_]

I think this video explains why you can't make the perfect circle in Minecraft :}

[@adamlau9274]

I actually like the rainbow glass without the beacons too looks like some cool colourful crystals

[@lone.faerie]

You just made ray marching in Minecraft... for a beacon. You're channel never fails to blow my mind

[@jasperdiscovers]

That was awesome! Love how it all comes together in the end.

[@mikivini73]

Congrats for the thumbnail, that was one of the most interesting videos i haven't search for Gj

[@kieran461]

I put off watching this video every time it came up on my recommended thinking "that's dumb yes you can" and never have I felt so stupid

[@rajczak_wonsz]

Best thing to watch at 2am while having a mental brakedown. I'll 100% use this in my survival world when I get better

[@FreakinGrooves]

i like this video, it's genuine and interesting and comes from passion, which you can't really say about most other minecraft videos these days ;)

[@JadeSadiky]

I think filling in all of the corners of the original circle would help a lot and would still look good from the outside

[@joeg579]

it definitely would not look good from the inside, those regions with less "beacon density" than the cardinal directions would now have more "beacon density" than the cardinal directions and you're left with the same issue

[@_Chrono174]

I think it would also be possible to solve it by increasing the radius of the circle, perhaps with twice the circumference, doubling each color, or leaving spaces between each beacon (if you don't have so much material), so since the blocks are further away, it would be less noticeable the irregularity between the beacons, the advantage of this is that even from the outside or not being in the center, it would be possible to see the shape.

[@EnderMega]

You said no one is going to make it, so just because of that Im going to make one.

[@squibble111]

if you want the armor stand doohickey itll probbaly be in the discord server in a bit

[@whateverprecisely]

Cake you won't bake is a perfect analogy lol. Very small difference but a noticable one. I thought this might be about effect area usefulness but colors are pretty cool too. Good video!

[@NameForHire]

This is how I'd imagine a 4th dimensional tutorial video to be like with the abstract circle

[@Electric0eye]

This is the most fascinating bit of information I will probably never need

[@sepiasmith5065]

this is SO FREAKING COOL wow that solution with the armor stand is so fascinating

[@samloredescarregado1755]

That video and the color grading one actually helped on the end barrens I were trying to convert each discovered island in a gimmick and the island that i woulf focus on beacon messed me up when i tried to make bigger circles with degrade Thanks, hope you get even more recognization

[@MichaKolb]

that's the amazing fusion of creativity an technicalities, that I love about this game. Thanks for sharing this with me!

[@davidgustafson6164]

The thumbnail and title of this video are perfect. Stuff like this is really clickable. Also the video was great :)

[@overestimatedforesight]

"It's best to consider this a baking tutorial for a cake you'll never bake" is unexpectedly poetic

[@Spec7rejay]

Actual interaction: Me: I need to play Minecraft Brother: what’s wrong? Me: I need to play Minecraft

[@pinkius]

That's why Hexagons are the Bestagons. If Minecraft was made with Hexagons, then you could've made semi-perfect circle.

[@Digitalsurfer265]

I love the off and on sequence, it’s like a light show

[@Skeletor96ba]

i am in love with the flightspeed changer and i've only seen it be used for a total of 2 seconds

[@mother_foxxer]

i haven't played minecraft since before they added beacons. why am i here. keep doing what you're doing i feel like i learned a lot that i will never use in my life.

[@peterpumpkineater6928]

You haven’t played Minecraft since 12 years so?

[@Burningurns]

I don’t usually watch much minecraft content but I’m glad I watched this. You are very talented, I love your building style

[@some_1214]

math time: i think this process can be done more efficiently when using complex argand functions and circles. starting with complex numbers: the function [a•cis(z)] where “a” is the distance from the centre and “z” is the angle relative to the positive x axis (with a range of -pi

[@poliax7066]

That's actually really cool

[@Jord_OP]

That is just beautiful

[@DanatronOne]

This could've been solved mathematically instead of experimentally! What you're effectively doing is trying to find good rational approximations of various irrationals. What you want to do is subdivide a circle into 96 evenly spaced units (for the 96 beacon colours), meaning each turn (such as for your armour stand) is 3.75 degrees. You have two conflicting requirements here, that are probably best expressed via a triangle. - You want to draw a right angled triangle with an angle (theta) as close as possible to each of those 3.75 degree increments - The hypotenuse of each triangle (aka radius of the circle) must be roughly equal (that is to say, you don't a drastically difference between each beacon; you want to find integers that are in the same ballpark) Additionally, the width and height of this triangle must be integers (since it's in minecraft, they're snapped to an integer grid) A standard "minecraft circle" is one that only cares about a consistent radius (hypotenuse). You care much more about there being a consistent 3.75 degrees between each beam. This is a mathematical approach to the experimental solution you found using the armour stand and raycasting, which can be generalised to many use-cases. You also only need to do 1/8th of a full circle, as you can mirror that to get a quarter-circle, and rotate that around to get the full thing. This means that instead of 96 coordinate pairs, you only really need to find 12 (well, 13, fenceposting for the diagonal). Starting from 0 degrees, and increasing 3.75 degrees each time, until you reach 45 degrees. To convert a degree angle into a pair of coordinates (let's use 30 degrees for example) you would have to convert it to radians (0.523598776...) and then find the tangent of that (0.577350269...). This gives you a decimal value (that's not necessarily rational). What you want is a rational (fractional) approximation of this value. Minecraft blocks are locked to an integer coordinate grid, which means you can only move a whole number of blocks in each direction. Obviously 5773/10000 would be a decent approximation of 0.5773, which would correspond to placing a beacon at the coordinate (5773, 10000). However that would place the beacon over 10,000 blocks away, well outside render distance, which isn't the best for visibility... also, we can get better approximations. You want to keep the denominator of this ratio relatively low, while maintaining as much accuracy as possible. For this, you can use a Farey sequence, implementing a Continued Fraction algorithm (google those terms for more info). These algorithms tell us that fractions such as 4/7 and 11/19 are good approximations of our 0.5773... decimal. We can check these with a trig calculator (omnicalculator has a good one) - plug in those values for the height and width of a triangle, and see that it has an angle pretty close to our target of 30 degrees. If we draw this visually, we can see how accurate it really is; i.imgur.com/LX8fsZz.png You say that this information is useful to almost nobody, but it's the opposite! What you're seeking by asking this question is something incredibly useful, and was a question asked by Euclid, around 2300 years ago! If you've ever used 22/7 as an approximation for pi, this is the branch of mathematics you have to thank for it.

[@coconuttv4454]

Why is this making feel so nostalgic, I think its his voice it fits the old calming Minecraft videos back in the day.

[@katebirch1207]

Interesting video, definitely came here because of the technical looking thumbnail, I got curious. (So far my biggest finished build is like a 6×6×8 house, so kind of out of my scale) Lovely end build, btw!

[@squibble111]

Thank you!

[@JayceMinecraft]

I love how you overdid this but I literally can't see a difference between the two LOLLL

[@whataboutthetrout5906]

I’ve watched this once already, but it came back into my recommended and its very interesting. A 10/10, trout fuckin with it

[@tyrannosaurusrekt1127]

i'm certain there's some really useful real-world application for this math problem you just solved that nobody else bothered to look for. like, there's gotta be.

[@Jack-ck3jh]

I'm admiring the fact that it looks chaotic until you stand in the middle and it all looks perfect.

[@AureaTW]

0:00 slime rancher ost, good choice. amazing choice even

[@mehhtep7002]

Inside: "Woah! That's trippy!" Outside: "Ba-dong"