Happy March 31st!

very useful for my mob farms that are insufficient by 1.01%

“Why are your tunnels 20-25° askew?” “Makes it easier to run from mobs”

Note this means that in order to escape something really fast pathing across the ground in Minecraft, you shouldn't be running in a straight line or diagonally but 20-25 degrees away from a straight line.

I feel like this is the perfect kind of content to make a kid who is kind of into minecraft actually find an interest in math

This isn't taxicab geometry but the chessboard geometry (named after the movement of kings or queens), known in math spaces as the chebyshev metric

As someone that thoroughly enjoys overcomplicating farms & avoiding typical "out of the box" tutorials, this content resonates extremely well with me. Sub'd !

Chebyshev distance! Honestly when designing AI based farms (not a big fan) I usually timed mob lifetime and was spawning them manually around the outer edge finding where it's the needed value, usually for pigman farms in the end it was a shape looking like a mandelbrot set instead of a half circle, not sure if you did practical tests for this video

For those of you wondering, distance between two coordinates here would be equal to max(x,z)+min(x,z)(sqrt(2)-1) where x and z represent the positive difference between the coordinates along the respective axes. Adding this to my list of distance types! Euclidean, Manhattan, Chebyshev, and now Minecraft(?)!

It's amazing how you innovate in areas we don't even think about

If we're familiar with L_p norms, then the L_(10/3) norm seems to be a good approximation to the metric described in the video. For a summary, L_1 is taxicab geometry, L_2 is Euclidean geometry and L_infinity is Chebyshev geometry. The formula for pi in this case is given by: 2*integral_0^1 (1 + (x^(10/3)/(1 - x^(10/3)))^(7/3))^(3/10) dx, which is very close to 3.31 (check with wolfram alpha). And if you plot the unit ball onto desmos |x|^(10/3) + |y|^(10/3) = 1, you get a very similar looking 'squircle' to the shape in the video. Edit: noticing some answers saying that this is Chebyshev geometry - not quite because the time taken to walk a diagonal is NOT the same as the time taken to walk orthogonally (compare with a king on a chessboard for instance). But it's not quite Euclidean geometry either, because the zombies don't walk in a straight line. So the answer lies somewhere between L_2 (Euclidean) and L_infinity (chebyshev). And it turns out that L_(10/3) fits the bill.

watched your vanilla skyblock series on the old channel so long ago, super pleased to see the algorithm has fed me this video to lead me back here. glad to see you're still around.

Not only does the spawning pad look cooler, it's also more efficient.

That’s a really cool analysis!

great execution of a unique idea. your channel is going places, sir. (and now i'm gonna binge your other videos lol)

You get your honorable spot in "might be useful later" playlist

Imagine if a farm was 0.5% away from reaching maximum efficiency...

you might know this already, but using the carpet ai_tracker module you can display the path finding of mobs!

im so happy that i found this small channel , this is top tier content and i hope you had a great pi day (you tube recommended was a bit slow )

That's what I love about sandbox games such as Minecraft : when you take advantage of the game's mechanics to do the most efficient farm, there's always something to discover to make it even more efficient than before, and after exploiting every mechanics, after optimizing the number of blocks or the space your design takes, after doing it in the most convenient place in the most practical way, you can still improve it by understanding how the games calculate things as basic as the path finding of mobs to make the platform the most efficient for their path finding. That's incredible.

4:10 They are called sectors. A sector is a part of a circle, delimited by two of its radiuses. A segment is a part of a circle, delimited by its chord

4:11 - For the eighth of a circle, I'd borrow from our lovely musician friends and say hemi-demi-semi-circle. 😂

Love how you just notice something in minecraft and start a study about it. I do it sometimes as well, but with everyday stuff

I remember gnembon did a video on this topic a long time ago but I keep falling asleep. Your explanation is much cleaner and understandable for me 😅

4:12 Reasonably sure that an eighth of a circle would be a hemidemisemicircle.

Super cool stuff man, good job!

wtf i stumbled onto this video and its genuis i love looking at technical parts of video games and i havent seen anyone else do this in minecraft idk hope you keep making content and also Erin Go Bragh

This is such a fun and weird channel, I also want to have so much fun messing around in minecraft! :D too bad I don't have a math background.

you're growing like crazy! Well-deserved!

I wonder how this will shape the oldschool donut gold farms as these are freakishly hard to build without external tools.

In StarCraft, the distance function is very simple to save resources. It requires no divisions or square roots (the divisions in the source code are compiled to bitshifts) and uses a linear approximation of distance mirrored a few times. The result is that a curve of constant distance from a point is not a circle but instead (approximately) a regular dodecagon. The distance function takes an ordered pair data type called an xy which has the differences in the x- and y-coordinates of the two points in fixed-point 8.8 binary format and returns an approximation of the Euclidean length of the xy. It looks like this: int xy_length(xy vec) const { unsigned int x = std::abs(vec.x); unsigned int y = std::abs(vec.y); if (x < y) std::swap(x, y); if (x / 4 < y) x = x - x / 16 + y * 3 / 8 - x / 64 + y * 3 / 256; return x; } So in the first quadrant, if y > x/4 or x > y/4, it just uses that larger value. If not, it will use a line with slope of -236/99 = -2.3838... if x is larger or -99/236 ≈ -0.419491 if y is larger, with this reflected for the other three quadrants. The endpoints almost meet up, but not quite due to the rounding built into the calculation. It's extremely efficient and surprisingly convincing in practice, though it does cause a lot of headaches for AI-controlled units. Additionally, although there are 256 possible angles in StarCraft (32 of which have unique sprites), most of the time units only move along the 8 primary directions, at least if they are traveling any significant distance and don't encounter an obstacle. However, although they can only move in 8 directions, they still move at a roughly constant speed (in the Euclidean sense), so it still takes longer to move along the diagonal of a square than one of its sides. So you don't get this King's-move behavior.

Woah ive been watching u for a while so this video is especially cool lol

Sectors, segments, and arcs are the words you're looking for

Wow the KZfaq algo is weird. Recommends a bunch of weird stuff but glad it recommended this! Great video, good content, pace and feel. You rattling off Pi at the end was disgusting lol Great stuff please keep it up, got a new sub!

"there's no pi on this 4-func calculator" ... "oh yeah" *types it* my favorite reason I learned a bunch of pi

I just stumbled onto your channel, I've been out of the Minecraft dev scene for a while, but damn, i love this video. idk if its how you speak or something but, for real, good video

Man i was impressed when you went past the 50th diget, i can only do up to 3.141592653589793238462643383279 (31 digets if i can count correctly)

amazing video man keep it up!!!

this video snipes the sweetspot of my brain that has a weirdly vested interest in both math and minecraft

This is genuinely the best Minecraft farm video I have seen in years. You earned yourself another sub!

The taxicab analogy forgets one aspect, that being that the distance covered still takes time. The mobs walk the same distance across diagonals, meaning it may be slightly less efficient to have the mobs travel along the diagonals.

I really like your energy and general curiosity. Thank you for lighting up my day

Wow this is really interesting! Super cool use of math tailored to minecraft!

Fascinating, this is some unique pi day content right here!

I loved all the analysis and math, and then finding an application for it all in making the farms fractionally more efficient

"Today I was playing Minecraft and decided to calculate Pi." Also, making the title "... increasse by 1%" was zero click bait, nice!

this video should've totally been 6:28 long for 2*pi

cool, i love these sorts of pathfinding farms and optimizations!

minecraft's william osman in all seriousness this is very interesting, just when you thought we had gotten the "perfect" farm someone comes up with this tiny optimization

This stuff is really cool that I doubt most others think about. Keep it up

This is such a good example of why non-euclidean metrics are useful! This channel is everything I ever wanted ❤

easiest subscribe of my life. i was really hoping to see more minecraft videos when i clicked your channel, instead of more pi videos (i mean, with the passion you speak about it, it could have went either way). was not disappointed !

very interesting and informative video, thanks!

they live in a world where circles are octagons, truly terrifying

Thanks for sharing your parrot project at the end, I didn't know they were telling you the nuclear launch codes!

As far as I'm aware, 1/8th of a circle would just be a sector!

@0:36 "sort of weirder diagonal" the word you are looking for is "oblique".

matt parker might be a bit happy that his hand calculated pi's can be closer to minecraft's pi XDD

Nobody has commented this yet, but all of the digits of pi at the end are correct! Great job Chris!

Such a great content! For the whole video I thought you have at least 100k views. Very underrated, keep going!

You remind me somewhat of SethBling, I remember really enjoying his content like this, digging into how the game works.

This knowledge will be applied to villager operated farms and bee farms, increasing productivity by 1% or more. 😊

As far as I can tell, the distance formula in this model is |x - y| + sqrt(2) min(x, y)

I don't know how I haven't noticed that zombies only walked in 8 directions. I've been playing this damn game since before zombies were even added!

Funny you measured the radius when talking about pi. People cant help but align with the more natural tau :P

another application for this specific kind of movement is tabletop gaming, like D&D or Warhammer, where minis are confined to the grid, and moving diagonal 1 block is considered the same as moving 1 block along the grid (depending on the rules; in some games/editions, a diagonal move might count as double movement instead)

By the way, I got a different value of pi than you. Area of an octagon I believe is 2 sqrt(2) r^2 (where r is the major radius), which lines up pretty nicely with πr^2, so π = 2 sqrt2 ≈ 2.83 So I guess I'll see you on Feb 83rd!

It is call "60 degree arc" nice video! 4:20

really enjoyed the video! what you're reffering to is also more formally denoted as "Manhattan Distance" (might give better search results idk) I researched a lot on this topic when doing distance functions for a crosshair builder I was working on while in college. also, I love to see people finding out these sorts of things that are genuinely interesting; It's something I wouldn't expect to see in a Minecraft video. color me pleasantly surprised and satisfied.

I don't even care about the farm I just clicked the video bc the title was too good

That is... a lot more pi than I have memorized! Though you happened to pause for a sec right after the last number I know.

Hemidemisemicircle: one eighth of a circle

this is really cute and informative :>

We do see the Zombie Pigman walk a 2 block long diagonal or just half diagonal in the beginning though, so they can go in 16 directions.

I think mobs used to walk in straight lines in older versions. Since when can mobs only walk in 8 directions?

Knowing that there is a minimum distance in the real world at the planck length(1.6*10^-31m), does that mean that there is a degree to which pi can be rounded that does not impact measurements in the real world?

The end of the video makes me think "NEEERRRRRDD" XD

2:55 this reminds me of Snell's Law, wonder if it'd apply here somehow

the relevant google search term would be "metric space" btw, or maybe "taxicab metric"

Oh my god I never knew you kept making videos. I'm still subscribed to RedstoneJazz lol

My head is spinning and I like it

6:03 He's having pi transmitted to him via beads in his colon. He's cheating. XD /j

Does it turn out to be practically true that zombies take the same time to move along a diagonal as straight, or do they actually take longer by a factor of sqrt(2), or is it something weirder?

elaborate reason to flex the memorization of pi

cant wait for zombie pi day

it's not that they can only can go in 8 directions. it's that they follow the pathfinding waypoints that happen to always be adjacent blocks

this is _revolutionary_ :)

Yo nice umbrella my guy

I don't know who you are but that was fun, thanks

@Vsauce Michael this is pretty cool

But Pi in the Minecraft world is 4. Make the best Minecraft approximation of a circle and count the outside edge (circumference) then divided by the diameter. =4 Make sure you are counting the outside edges, not the just the number of blocks. At corners a single block will contribute 2 sides to the length of the circumference. In a world with only 90degree angles, pi = 4.

This was phenomenal!

funny how i discovered this video on march 31st

This is cool, I like this content.

you have a beautiful voice! also the minecraft stuff is cool

Ayo my man worked out the MC metric 🤔😎🗿

Well done!

π = ~2.8 for this circle if you use the equation 2πr There are ~96 blocks on the perimeter, and the diameter is 34 or 35, so Pi comes out to be around 2.8 It's actually a pretty big difference, even though this seems to be a pretty good approximation of a circle

how is there people like mumbo or etho, or the guys from scicraft.. but this gorgeous man with a medieval clock as his beds footend is discovering sh*t that ive never seen before no hate, all love this blows my mind

imagine this dude would be your math teacher