270-year-old math problem SOLVED! Grazing goat problem

[@uumlaut-]

"ok, how are we doing on the problem solving?" "the goat is now in 6 dimensions"

[@savannah7375]

😂😂😂 my favorite comment

[@jezwilde2376]

Brilliant. 😅You gonna have to rein that in guys

[@joshuaohuka7719]

​@@jezwilde2376👏🏾👏🏾👏🏾👏🏾👏🏾

[@dinozaurpickupline4221]

Obviously it's a pun But we can put goat anywhere even in our digestive tracts

[@luisalvarez8266]

😂

[@theoneafterthelast]

Mom! The 5 Dimensional Goat is eating our grass again.

[@javed_19_05.]

😂

[@pedroaugusto656]

Mom: "it's just a goat" Child: "No, it's a fucking goat"

[@Ashar121]

I read that wrong and it threw me for a second

[@theoneafterthelast]

@@Ashar121 lol, I need to know how you read it.

[@Ashar121]

@theoneafterthelast lets just say I missed a couple letters from "grass"

[@nabinnyc]

Multidimensional Goat: "So long, and thanks for half the grass." 🐐

[@bartimaeu1]

Took him a mere 42 hours

[@g4mmalotus937]

Too bad our time has gone so fast We tried to warn you all but oh deaaar

[@TeamDoc312]

And the goat is tattooed with the phrase "Don't Panic!".

[@shanshansan]

Farmer: "I need this grazing goat to only cover half an acre, but it would have to be tied to a rope on a point. Could you help me?" Person: "Sure, shouldn't be that hard." 270 years later:

[@Unstpbl]

And then the goat just chews through the rope and sets itself free

[@advaitkamath8442]

"Hey, how yea doing, I noticed you haven't left your house for a couple yea-" " *THE GOAT IS NOW IN THE 5 DIMENSION* "

[@brooklyna007]

well you could approximate it with some simple methods probably by 400 BC. 500 BC the discovery of the area of a circle was made. Then you just need to binary search with successive approximatons.

[@ignorasmus]

As an engineer, I and my colleagues would advise the mathematicians to just put up a fence on half the field or just tie the goat in the center 💁‍♂️

[@pasikavecpruhovany7777]

As a fellow engineer, I'd suggest to put two goats in there.

[@andrewguthrie2]

As a mathematician I'd say this is evidence for the conjecture that all engineers' grammar is appalling. "My colleagues and I..." "I'd suggest putting..."

[@WokerThanThou]

As a communist, I'd put all the goats in there and tell them it's for the greater good.

[@andrewguthrie2]

@@Lee5p33dy Let's keep it light.

[@primenumberbuster404]

​@@Lee5p33dy ok blondie.

[@josome7451]

"Mathematicians found it much more fun imagining the goat in a multi-dimensional sphere, rather than solving the problem."

[@tonilobaaladeitan2770]

Just find the radius, then use that measurement starting from the side

[@rhot2963]

​@@tonilobaaladeitan2770I think you miss the point there. It is difficult to search the length from an area in this problem😅

[@tirramasu7948]

Why don't they just use a real goat? Like, I know it sounds ignorant But you should try to test the hypothesis before stumping around 300 years worth of mathematicians

[@lastsong7159]

​​@@tirramasu7948it's a simplified hypothetical. The issue isn't the goat eating grass the issue is that in terms of math, we simply did not have an equation or concept to resolve the issue. Like how black holes mathematically can't exist, but of course physically we know they exist because we can observe them. The problem with black holes is the same issue with this goat problem. We know it's a real thing, the math for it doesn't exist yet to explain it though, but other sciences do.

[@advaitkamath8442]

​@@tirramasu7948that would give an approximate solution

[@Internet_surfer.]

Interviewer: "So what are your strengths?" Mathematician: "I can find problems in simple things."

[@crispyandspicy6813]

This is the exact reason why you never buy land in circular shapes

[@user-dk8mj4uo9c]

With square shape it's almost as bad, the rope is the main problem

[@barryon8706]

Do we need to assume a spherical goat?

[@andrewguthrie2]

Light, inextensible and also a perfect logician.

[@iamdigory]

Nope, harder, a zero dimensional goat

[@thefrenchguard6999]

Assume a goat that isnt tied up but one that understands English and mathematics better than we do. He is instructed to only eat the correct blades of grass.

[@jorgesalazar2583]

That is a physicist's approach

[@deus_ex_machina_]

We need to imagine a four-dimensional hypergoat projected onto a three-dimensional globe.

[@alaxion5628]

"all I ask for is infinite precision, is that so much to ask for?" -mathematics

[@jefflittle8913]

As it turns out, just a tiny bit too much...

[@gardengnome3249]

What's the difference between precision and infinite precision?

[@vbgvbg1133]

@@gardengnome3249 precision can be measured up to a certain degree. infinite precision is simply precision to an infinite degree

[@gardengnome3249]

@@vbgvbg1133 Sounds like kamala harris giving a speech.

[@random6033]

id just brute force it, cause i dont need infinite precision

[@EebstertheGreat]

There are a few mistakes here. 1. The bounds of integration are wrong. As Ullisch published in a correction, the curves should be |z−3π/4| = π/4, not |z−3π/8| = π/4. 2. This was not the first exact solution, and other solutions were not approximate. The transcendental equation here is (2−r²) arccos(r/2) + r√(1−r²/4) = π/2. There are plenty of ways to solve this exactly for r, including Newton's method. The solutions just don't have a closed form. 3. It's not clear in what sense the solution given here is a "closed form" anyway. It is written as a ratio of contour integrals. And the easiest way to solve these contour integrals is to solve that underlying transcendental equation or an equivalent one. So this is just rewriting the problem in a more complicated form. There is still no finitary method for getting a solution. I think this gets to the question of what counts as a "solution." Herbert Wilf asked something similar for combinatorics. If the "answer" (here the ratio of contour integrals) is more complicated to evaluate than the original question (the transcendental equation), in what sense is it really an answer?

[@crossintegrals]

I cannot understand this for now but I will like the comment.

[@scrumptious9673]

💪

[@Adomas_B]

Well it's in a nicer form than an infinite sum ir something like that. I don't think there even is a nice solution, the equation is TRANSCENDENTAL, and dealing with that area of math 'closed form' is usually impossible

[@EebstertheGreat]

@@Adomas_B I think an infinite sum could be superior. It is easier to compute. Any contour integral is just going to be turned into a sum before computation anyway. But I agree that there probably is no actual closed-form solution. I find it very odd that this integral expression was described that way, since that isn't usually what the term means.

[@MrSkinnyWhale]

Indubitably

[@BunkerSquirrel]

Remember kids: calculus is the wizardry of the math world. Strive to learn it, it’ll change your life forever.

[@sgvincent100]

I failed calculus three times. That changed my life forever.

[@IhateAlot718]

When I learned calculus for the first time and realized all my algebra equations could of been solved much quicker using derviviates, I broke my pencil and was mad as hell. Lol.

[@_tsu_]

Multidimentional grazing got me cracking up fr

[@TradieTrev]

Have you seen how goats pupils are square? They are born flat earthers lol

[@thefrenchguard6999]

Adding dimensions to make something easier blows my mind.

[@zechariah22]

I mean, a hay bale is kind of like 3 dimensional grazing

[@Phoenix-gd4xw]

Seriously 🤣🤣

[@juanit0tackit0tackito2]

the Kingdom of GOD is coming…“Silver is for the kettle, and gold for the furnace, but The LORD is the tester of hearts- Bible” your heart is like discovered silver, dirty and not pure, when silver is purified it is melted over and over, to the point that when it’s melted and glows red hot, it is pure enough to see your own reflection in the puddle, so also does the LORD purify your heart, till HE can see HIS own reflection in it, seek the LORD and be reborn, ask The LORD to renew and restore you, repent and be baptized for the forgiveness of sins, Jesus died so that our sins will be wiped away and so that we could be made new, if would be wise you would be wise for yourself, pick up your cross and deny your flesh and follow the path of GOD, for The Kingdom of GOD is at hand, in JESUS MIGHTY NAME Amen and Amen

[@siegesouth]

As soon as I heard “exactly half of the acre” i knew that shit gon be a whole meal made of pi

[@Aaa-vp6ug]

Delicious!

[@brettknighten1171]

Convert acres to sqft to make it easier to visualize

[@siegesouth]

@@brettknighten1171 that isn’t gonna help shit in something like this

[@nodrance]

See you take a sin and cos and knvert the integral and for some reason the answer is pi^pi divided by the square root of the golden ratio. Also e showed up

[@EIGatito]

Yo buddy

[@shababdidar]

I misread the title as "270 year old math problem solved by goat"

[@ZimVerse]

That sounds pretty accurate tho?

[@mail-fuer-band]

Mathematicans really need to touch that grass

[@parrampampam]

So what did the goat eat for the past 270 years then?

[@daveseddon5227]

All the grass outside the fence. That's why they put the fence up.

[@andrewguthrie2]

Wolves were eating all the goats until they solved the river problem.

[@parkerbond9400]

The other half

[@SiddharthRaiyani]

Goat will have to starve till the half an acre of grass regrows again.

[@asa-punkatsouthvinland7145]

Everything

[@necromanticer169]

I tried solving this problem in high school for an approximation of how to bite exactly half a cookie 😂

[@SamuelDimitrov]

rip lmao

[@tompw3141]

Get your teeth straightened... Into a line. Much easier that way.

[@gmail.com39510]

Cut the cookie in half 🤯

[@ikhlasulkamal5245]

Ah yes, A Trancendental Hyper Dimension Cookie sounds great for a highscool student

[@necromanticer169]

@ikhlasulkamal5245 I had no idea of the scope of the problem when I began. I was just playing with shapes and relationships and realized that Calculus could relate the area of shapes. I never fully understood how to apply calculus, but the application is rarely the true benefit of calculus.

[@itsmealex8959]

As an economist, I would just sell the goat

[@pantanlp7187]

Instructions unclear i have a goat living in a 10 dimensional space now

[@Koopaperson]

Engineers: Just build a second fence cutting the area in half Mathematicians:

[@geoffreyparker926]

Engineers: 1 Mathematicians: 0 Doh

[@babelbabel2419]

You should be a politician haha. The art of not answering the question and diverting to a question to which you know the answer. But that's not science anymore ;p

[@velvetypotato711]

the question is framed as a goat and field but there are other applications for the idea where a fence might not work

[@cipherxen2]

Engineers won't need 270 years, they'll get an approximation in 27 seconds and be happy with it.

[@davidioanhedges]

Approximations are easy ... Exact results are much much harder, and sometimes mean that the approximate solutions are utterly redundant

[@lonestarr1490]

Yes. And they learn nothing in the process. It might sound strange, but finding a solution is not the same thing as solving the problem. And you know what? All the formulae you utilize to arrive at your approximations stem from mathematicians who weren't satisfied with "close enough".

[@cipherxen2]

@@lonestarr1490 say what you want. But engineers built this world as we know it.

[@asdfasdfasdf1218]

Approximations are not the sole purview of engineers. Mathematicians concern themselves with approximations just as much, namely in field called numerical methods. It's this branch of mathematics that is responsible for creating better and better simulations of physics and other systems. The one area that must be exact in mathematics is logical reasoning. That is, an approximation is only justified to the extent it's proven to be close enough.

[@lonestarr1490]

@@cipherxen2 Based on formulae found by mathematicians who weren't content with "close enough".

[@shirkedance]

never knew my Farmer friends were Maths geniuses

[@ihaveaname15]

This is why you go outside and do it instead of procrastinating.

[@Avaricumstudios]

That mathematician is the GOAT

[@Seth-vj8vm]

Shut up, take my like, and go home.

[@nickjack1696]

Yes, he was fed up that no one had figured it out and let him graze so he did it himself

[@voltsp288]

​@@Seth-vj8vmliterally it's just perfect

[@yakuzzi35]

My toxic trait is never believing anything is complex until I try it myself

[@jefflittle8913]

That is no more toxic then not believing weights in the gym are too heavy.

[@nickhosford7801]

This was me.😂 "That can't be that complicated! All you do is take the length as a radius and... wait... but then you have to... oh... and then account for... dang... ok.

[@2nd-place]

That works for me, until it doesn’t. And half the fun is figuring out when you’ve gone too far! It’s especially fun when you’ve taken something apart that you definitely shouldn’t have.

[@snared_]

So this was interesting, I paused after the description to work on the problem because it sounds trivial. So I set to work and tried the first obvious thing - using the formula for a circle and the inverse as sqrt(1-x^2), I was able to write down an integral equation of only constants and a variable r, the length of the rope. This alone solves the problem if you believe in rapid convergence of this via any classical iterative method (AKA you are sane), but if you DON'T believe that, you can just use the fundamental theorem of calculus, and some hand calculations to show that the integrand doesn't change fast enough to feign any 'exact answer checker' program. Anyway, clickbait as usual from this channel. By the way, the proof is even cleaner if you are able to integrate the function (Which to be honest I did not do, bc its not necessary). If that took genius mathematicians 270 years and me, just some recreational medication and an afternoon with chalk, then this world is seriously fucked up beyond belief. So yeah, that trait is not toxic. If you had it, then maybe you would have solved this problem like I did!

[@bobgoldham69]

@@snared_ The problem being that your solution is wrong. You're essentially dealing with overlapping circles, which are already notoriously difficult to describe and then add in the complication of having to perform the inverse operation on a complex system of equations and then go find an exact numerical solution.

[@mcanna5115]

Mathematicians have the weirdest problems

[@omarjassar4650]

Now I understand why people don't build circular fences , thank you 😊😊😊

[@SDZ675]

Mathematicians seeing a goat outside: "How can we turn this into a complicated 270 year old problem?"

[@JayQwery]

Yeah I know just let the goat eat!

[@Dsay_Diablo_27s]

Yes its very simple logically you can have any length wait till the goat eat half acres of grass then stop the goat. Why they did calculation is this stuff A ten year boy can tell it Don't tell me the area should be circular Cause then assume length of rope to be x Then find the general area for x length and put it equal to half acre Problem solved Btw yes its tough to find area for general x 😢

[@JayQwery]

@@Dsay_Diablo_27s That's why the mathmatic problem is a lot more complicated then just figuring out a general awnser lol.

[@egggg000]

As someone who has PhD in Mathematics, I want to tell you that let the goat eat as much it needs. Don't pressurise it. ✌️

[@outandabout259]

pressurising a goat sounds painful.

[@alexjames1146]

It could explode.

[@luisalvarez8266]

Talk about peer pressure

[@rey1242]

No, pressurise it, exactly at 1 atm.

[@OokamiKageGinGetsu]

"Don't pressurize it." So, how many PSI should my goat have?

[@sayanneogy3079]

GOAT Problems Require GOAT Solutions!

[@JessYoutubeAccount]

"Complexity can be lurking in the most unexpected places." People, particularly online, need to take this to heart before speaking on subjects they don't understand. Great quote!

[@ARockRaider]

true, but mathematicians also dream up the strangest problems to try and work out. like if someone came to me asking this question i would want to know why simply having the rope be the radius wouldn't do. or better yet, why are you tieing an animal already inside a pen.

[@justtocomment4100]

The man who asked the mathematician this question 270 years ago probably doesn't need the answer anymore.

[@MrIshtiaqkunda]

😂😂😂

[@absentspaghetti4527]

Turns out that while you were solving the problem, the goat chewed through the leash and ate all of the grass, congratulations

[@EEEEEEEE]

E‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

[@ayuballena8217]

now the goat has ascended another dimension… again

[@Name_less_youtube]

My brain: depends, how big is the goat and how long is it’s neck?

[@cursedcat6467]

“Build a half acre enclosure”

[@RishavManiSharma]

The paper is "A Closed-Form Solution to the Geometric Goat Problem" by Ingo Ullisch.

[@ollllj]

"closed form" fraction of 2 integrals with lots of trigonometry.

[@noahprisament4190]

​@@olllljclosed form as opposed to numeric

[@agmhelena7266]

🤓👆 "um achually"

[@soyokou.2810]

As in not just "proven to exist satisfying this equations" or "will converge to a solution"

[@CafeMuyCaliente]

Inko Gnito ? No, Ingo Ullisch.

[@sidneymonteiro3670]

I have an exact solution but it requires a perfect vacuum, no friction, and spherical goats.

[@akshy471]

I'd smash next question

[@calebklingerman7902]

This is an example of when the uneducated farmer proves smarter than the mathematician

[@tonydai782]

And a larger margin to write the proof

[@TheOpticalFreak]

But then the goats would die! 😢

[@dave2.077]

you are one weird goat farmer thats for sure

[@TheNitesh2401]

Mathematics + Magicians = Mathematicians

[@hecker.13]

"Hell no bruh, let me just eat the freaking grass bruh" :-

[@Sphere723]

As an engineer I'd just set up a spreadsheet and iterate the length of the rope until the answer was 50% of the area. Lots of things in Engineering are like this where checking a design is way easier than coming up with the design, so you just iterate on the inputs until something works.

[@unrealuknow864]

just put the post in the center and then play with the length until you get to 50%

[@No_True_Scotsman]

Yeah... it would be trivial to get an answer with ridiculously high precision just by trial and error for anything practical.

[@tanjeeschuan4999]

The people who ask why are the ones who advances any field. Sure, you can just make a bridge that works good enough. But though analysis of designs and formulas, better bridges are built

[@turolretar]

@@tanjeeschuan4999oh come on we talking about a goat here

[@Centerboarder]

Nice one. Agree.

[@RYN988]

Philosophy major: what is a goat?

[@anthon33]

Ha ha!!💤

[@justmonika9936]

Underrated comment

[@OokamiKageGinGetsu]

English major: Tanngrisnir and Tanngnjóstr.

[@roymendez9054]

You must imagine the goat is happy

[@Lee_Enfield95]

More like, what is goatness?

[@roblowery3188]

Your branding is on point. Every single one of your videos is recognizable as your style. Just wish I knew about this recent breakthrough sooner. I just gave my goat away to a needy family and sold my circular lot in Scranton, PA to pay for my KZbin subscription. Damn shame.

[@kormagogthedestroyer]

Solution: make the rope the diameter of the circle, and tie the other end of the rope to the other side of the fence instead of the goat

[@i_never_had_a_burger]

"This problem sounds so easy, I'll try solving it right now" "Oh..I think I'll just leave it"

[@filiperodrigues97]

Exactly my thoughts when I got the pencil and paper to try before watching the rest of the video; it was fun and games sketching the basics of the problem, until I got to a point where I was like "maybe I'd have to use some trig shit to get ahead, so nah I'm good bye"

[@lyde4899]

Hold on I might have an idea

[@heavenlypot]

That's what I did. I was about to pause it so that I don't accidentally see the solution but i was a tad bit late and saw that equation and... Took a chill pill 😂😂😂

[@snared_]

Lol I actually paused and was able to solve the whole problem from top to bottom. Trust me, I was laughing so hard afterward because the woman was saying it was impossible and unsolved for years. It's an amazing feeling to win at something someone else feels is impossible. It's like checkmating in chess

[@lyde4899]

@@snared_ Did you integrate the surface using the two curves as functions ? I did that

[@mattturner3484]

"some mathematicians tried to solve the problem by imagining a goat in a multimensional sphere"

[@SolvingSkills]

Making stuff up, calling them problems, and then spending centuries trying to solve it. Mathematicians are epic, i love them 😂

[@geoffreyparker926]

Same as Climate Changers.

[@eyeover7307]

you know this shit is hard when we going past the original dimensions to make it easier

[@francisluglio6611]

Lesson: Never underestimate multidimensional goats

[@metalheadmax09]

I have goats. All goats are multidimensional if they want to be.

[@francisluglio6611]

@@metalheadmax09 I love your username btw. 🤘

[@dimaratosgeorgiadis2672]

-I just got my phd in Math at Harvard -So you know a lot of Math? -''Cries inside''

[@ohasis8331]

Maybe goats are complicated creatures?

[@BerndSchnabl]

Finally. All the goat farmers were waiting feverishly for this 😂 just kidding. It's awesome 👍

[@chrisschembari2486]

Researchers stare at their blackboards, arguing over goat springiness and rope tensile strength. Goat chews through rope, eats the whole acre, unnoticed. Goat wins because ... it's the GOAT.

[@mk17173n]

This is the GOAT of math problems lol.

[@roberttelarket4934]

mk17173n: Ha ha!! Very very very clever!

[@juanit0tackit0tackito2]

the Kingdom of GOD is coming…“Silver is for the kettle, and gold for the furnace, but The LORD is the tester of hearts- Bible” your heart is like discovered silver, dirty and not pure, when silver is purified it is melted over and over, to the point that when it’s melted and glows red hot, it is pure enough to see your own reflection in the puddle, so also does the LORD purify your heart, till HE can see HIS own reflection in it, seek the LORD and be reborn, ask The LORD to renew and restore you, repent and be baptized for the forgiveness of sins, Jesus died so that our sins will be wiped away and so that we could be made new, if would be wise you would be wise for yourself, pick up your cross and deny your flesh and follow the path of GOD, for The Kingdom of GOD is at hand, in JESUS MIGHTY NAME Amen and Amen

[@jefflittle8913]

Leash your humor.

[@snared_]

So this was interesting, I paused after the description to work on the problem because it sounds trivial. So I set to work and tried the first obvious thing - using the formula for a circle and the inverse as sqrt(1-x^2), I was able to write down an integral equation of only constants and a variable r, the length of the rope. This alone solves the problem if you believe in rapid convergence of this via any classical iterative method (AKA you are sane), but if you DON'T believe that, you can just use the fundamental theorem of calculus, and some hand calculations to show that the integrand doesn't change fast enough to feign any 'exact answer checker' program. Anyway, clickbait as usual from this channel. By the way, the proof is even cleaner if you are able to integrate the function (Which to be honest I did not do, bc its not necessary). If that took genius mathematicians 270 years and me, just some recreational medication and an afternoon with chalk, then this world is seriously fucked up beyond belief. Anyway yeah it's not the GOAT of problems as it's quite small in the tools required to solve it. Once you fully understand the problem (and the higher dimension ones) you still haven't touched so much of the machinery we discover and maintain. A better GOAT candidate problem might be Riemann Zeta zeroes, as there is literally so many different areas of mathematics that it will lead you to that you will encounter even if you never heard of Riemann Zeta Zeroes specifically eventually.

[@jellomiki]

Daaaaamn Scott ! You got hot news on this one ! Well done my man !

[@abhishekpahariya8699]

Ask the goat if it is hungry enough

[@forksoverspoon10]

As a student, I'd suggest to let the goat have it's fill

[@rafaelgostosinho3769]

As a student, I'd suggest to put a fence dividing the area in half (sorry for the english 😅)

[@bencallister5500]

This is why I'm a nurse. The worst math I deal with is medication dosing.

[@jefflittle8913]

So how do you give your patient exactly half their dosage if it is spread as a layer of powder and they get to choose the length of straw to poke into the side of the dish?

[@Spencerx38]

​@@jefflittle8913I'd just give them full dosage, they're gonna die anyways 🤓

[@CrusaderTube]

Well, hope you get it right 😳

[@thomasdavidson2886]

that's some incredibly important math

[@markdaniel8740]

One of the leading causes of death in America, is hospitals giving the wrong dosages of medication. Please take math more seriously.

[@Ashboy1818]

The 5 legged goat is doing it again!!

[@Tonatiuth]

Maybe it was easier to step away from theory and actually get 1 acre to experiment with goats

[@TradieTrev]

My real world example is don't tether your goat, it may become entangled. Had a few pet goats over the years, treat them with love like a pet dog and they'll always come back and not stray too far from home untethered. Maths problem solved :P Love your work!

[@pasikavecpruhovany7777]

Not a great advice if you have neighbors with gardens, shrubs or small trees. The solution to tangling was to put a chain swivel on both sides. Another anecdote - we had a goat and a sheep and they acted like matter and antimatter. The sheep loved the goat and always wanted to be near her. The goat hated the sheep and always tried to stay away from her as far as possible. We had a nice system where we only had to tie the goat and the sheep would stay nerby... until one day it broke free and tried to outrun the sheep. Luckily police in a nearby city caught the sheep-propelled pair.

[@TradieTrev]

@@pasikavecpruhovany7777 Goats are sociable animals, that's a pisser of a story. Only time I got a phone call was from my neighbour (a plant nursery owner) they since erected a fence because if it wasn't the goats it'd be the roos eating the baby plants. Was always magic to watch the goats and roos hanging out together, they never bothered each other.

[@pasikavecpruhovany7777]

@@TradieTrev They tend to be but they have personality. The one I mentioned was quite introverted and kept it's distance :D

[@aluminiumknight4038]

Goats are food lol

[@frogpaste]

No, this is good advice. The last time I saw a tethered goat, a tyrannosaurus ate it.

[@Arthur-zz5cu]

Poor goat! It just wants love.

[@DarthGTB]

And grass. Mostly grass

[@helenesaintclere5639]

I think I saw this goat in the Monty Hall paradox . Poor goat is always the booby prize .

[@bishalnath4451]

@@DarthGTB Bro he was left hungry for 270 years.

[@padmeshpande7128]

awww

[@Ener-G]

This got me started on a math tangent and I have now realized just how many methods I have forgotten for solving for variables inside trig functions. I have a BS in math. I work with trig every day. Brain whyyyyyy

[@sethdon1100]

Apparently this single video let me down a rabbit hole so deep I eventually find out you can write down exact answers to transcendental equations using his method.

[@kintex6441]

I once remember my physics teacher telling us "There's no simplicity in life. There's just simplified questions, and shallow answers". I never took that as a diss, or him being a smartass. Quite the opposite, he was a pretty humbled dude. I later asked him what he meant, and he said something (Can't remember exactly, it was about 3 years ago) about how answering a question can be pretty easy, but rigorously proving it both theoretically and experimentally is the hard part.

[@captainjirk9564]

Sounds like the words of a man who knows the true definition of momentum

[@sunnicivang1093]

A real-life farmer: *Uses a rectangular acre of land.

[@djedg10]

The maths would be just as complex, given that the goat would trace a circle. In fact, the circular field simplified it a bit.

[@johntitor7600]

​@@djedg10 Not if you put it on a dog runner and it only reach half of the field. Still only connected to a single string but with a loop

[@S7orm89]

​@@djedg10 The complexity of the problem relies on the fact that the field is circular and therefore the area under the goat circle is difficult to calculate. With a square field if you tie the goat to the corner you need a √(2A/π) rope, where A is the area of the field. For example with a 100mx100m field you need 79.79m of rope.

[@madeofmandrake1748]

Yup. This sounds very similar to the problem of squaring a circle, or, taking the area of a circle and creating a square with the same area, using only a compass and straight edge.

[@Faheem1988]

my homework was eaten by a goat in other dimensions.

[@blazingazong]

Dude literally got that Greene’s theorem in the solution. I’m dead

[@snared_]

could you expand on that? I know of the theorem but it's not immediately obvious to me what it says here

[@blazingazong]

It’s a conversion from integrating a path along a vector field as a single variable integral, but it only works for straight paths Edit: it also happens to be notated by a regular integral symbol with a small circle in its center when an integral is compatible with the theorem

[@corrinflakes9659]

Imagine if this was a problem a goat owner friend to a mathematician really needed to know back then?

[@pSynth]

"You can make simple things complex it's the ability of mind" but i go for heart

[@anti-spiral159]

"You brought your homework?" "Yes right here it is" "It...just dissapeared in my hands" "Ah shoot-dang, the goat in the 6th dimension ate it again."

[@wildhunt3302]

Now let’s talk about how a 4th dimensional goat should graze half the grass on a 2 dimensional plane.

[@helenesaintclere5639]

Tibees will delve into that conundrum

[@x-lux1781]

Bro still didn’t tell me how long the rope needs to be

[@bunnykiller]

83 feet

[@yuresko1349]

I was a bit frustrated with myself that I couldn't solve this problem until I read the title

[@jerkycam]

Since she avoided explaining the actual equation I understood her explanation perfectly fine.

[@galuxistar1615]

The goat wondering what he should be doing when trapped in a multi-dimensional sphere.

[@vikingthedude]

The farming industry won’t ever be the same

[@essaboselin5252]

"First, assume we have a perfectly spherical goat..."

[@invaderg3332]

Multidimensional Goat: "So long suckers." (Took off to another dimension, after eating half the grass)

[@godforreal7355]

Hold up... Fence and turf are at a 90° angle, and we have to allow for the circumference of the goat's mouth...

[@brianzhang349]

And this is why engineers exist. Because the real world has a shocking amount of room for error.

[@r.mcdonnell8614]

When Americans did research in South America in the late 1800s, it was engineers from GA Tech, not mathematicians from the Ivy League who built the necessary transportation for the researchers from scraps and spare parts As a side note, it's how Ga Tech got the colloquial term "Ramblin' Wrecks", as discarded 1800s tractor parts did not make for the smoothest riding automobiles

[@diabl2master]

I'd like to understand what's so complicated about the 2D case. It feels straightforward.

[@BrianPellerin]

I am somehow convinced there is still a simpler solution but have absolutely no idea how

[@prajittr4933]

The mathematician who solved this is the GOAT 🐐

[@lm9327]

Nice pun :)

[@thidtle]

As someone who owns goats, just put up a fence divider if you really don't want half of it being eaten. Also do not put a rope or collar on your goat unless you are with them because it can strangle them

[@heronimousbrapson863]

To keep the goat from eating only half the acre, build a barrier through the centre. Some mathematicians have way too much time on their hands.

[@WeirdDuck781]

As a software developer I can truly tell you there is no such thing as a "simple problem"

[@NathanHedglin]

😂 yup

[@omgitzthunderlol4598]

As a minecrafter it’s called a fence and a ruler

[@ThatWhichObserves]

As an ignoramus, I can tell you there are always very simple problems. Sometimes those simple problems are people looking for the wrong answers.

[@Exit311]

No, in programming there are exactly three simple problems: 1. How to break a function 2. How to complicate a simple problem

[@Exit311]

Sorry but in programming there are three simple problems: 1. How to break a function 2. How to complicate a simple problem

[@romulusaikido]

So this is why I never met a mathematician that owns a goat.

[@rysus]

I wasn't listening closely to the first sentence and I was legit wondering "why is the fence *secular* ? Would it ever be religious?" 😂

[@Gbbb239]

Thank you. Some 21 years ago I was handed this math problem and couldn’t solve it. Thankfully I now know that it wasn’t trivial at all…

[@randomz5890]

This definitely did not seem like it would be that hard when you hear the question. It would be amazing if you could make a video explaining this.

[@upandatom]

There is one on numberphile

[@randomz5890]

@upandatom Oh, thank you for telling me. I think you doing it would bring something special to it, though. But really all I need is a video haha.

[@utsavman47]

I'll try explain it simply to the best of my understanding. What we're dealing with here is crescents. A cresent is formed by two circles over lapping (the grass field and the area of freedom of the goat). The formula to find the area of a crescent depends on the radii of both the circles. The area of the field circle is known, and the area of the crescent which the goat can't reach is known (half the circle). So you would think we can find the radius of the goat leash with the area of the crescent and its circles radius. But this formula uses some trigonometry. Now trigonometry becomes a little none sense when going in reverse. It's not straight forward like 2 + 2 = 6 - 2, so they couldn't use reverse trigonometry to find the radius of the goats leash. It took that many years to figure a work around through this obstacle. So yeah you can get area from length but getting length from area is harder. It's more of a testament to trignonometry's bullshit really 😂

[@roybiv7018]

​@@utsavman47Thank you for explaining it well to us non-math people.

[@ejb7969]

And even some of us mathier people.

[@Nicoricanmarxist]

I’m totally fucked because I started wondering how much grass does a goat graze on an hour.

[@ItchyKneeSon]

This is obviously a question for Marty and Moog...

[@xupingzheng682]

Dad! Your tummy has a fat goat in it! (*grows fat*)

[@ztoob8898]

When I run into (or even suspect I'm about to run into) a trancendental problem, I go straight to Excel and its "What If Analysis" tool -> "Goal Seek". Goal Seek will iterate modifying cell A to make cell B equal to a certain value. I set it up so cell B is 1E6 times the error and tell Goal Seek to make cell B = 0. That's plenty accurate for me. You guessed it: I'm an engineer.

[@Allen2]

Engineer or CPA (USA accountant)

[@Gatorofthyballs]

The goat is going places he even lives in 4d now

[@short_dose_of_internet]

GOAT for a reason

[@sotocsick3195]

I am in ninth grade and figured out the area of two intercepting circles. And I solved this in a month. From there on this was a really straight on problem. And I got the same solution in another two months. Wtf?

[@tradingmania5295]

It took so many years for a problem to be solved. But the world has progressed a lot in the last 100 years.

[@Freakinawesome333]

It's a good job I heard the "stumped mathematicians for 270 years" bit before pausing it and trying it myself 😂