Secrets of the NOTHING GRINDER

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This video is the result of me obsessing about pinning down the ultimate explanation for what is going on with the mysterious nothing grinder aka the do nothing machine aka the trammel of Archimedes. I think what I present in this video is it in this respect, but I let you be the judge. Featuring the Tusi couple (again), some really neat optical phenomenon based on the Tusi couple (I first encountered this here: • Crazy Circle Illusion! ), the ellipsograph and lots of original twists to an ancient theme.
Here is a link to a .zip archive containing 3d printable .stl files of the models featuring the Mathologer logo that I showed in the video: www.qedcat.com/misc/grinder.zip
I usually trim the corners and excess material off the (slightly slanted) vertical edges of the three sliders to make them run without catching on anything. I also sharpen the points of the pins a bit before pushing them into the sliders. They lock in place automatically, you don't have to glue them in.
Other 3d printable incarnations featuring different numbers of sliders are floating around on the net-for example search nothing grinder/do nothing machine/Archimedes trammel on www.thingiverse.com
The wiki page on the nothing grinder is also worth visiting: en.wikipedia.org/wiki/Trammel...
My current bout of nothing grinder obsession started with Naomi a year 10 student from Melbourne who did a week of mathematical work experience with me at Monash university a couple of weeks ago. As her project she chose to design a 3d printable version of the wooden model that you see in the video. Her Rhino3d files of the square and hexagon grinders served as the starting point for the models you can see in action in the video.
T-shirt: tinyurl.com/ybl55hez
As usual thank you very much to Marty and Danil for their help with this video.
Enjoy :)

[@BadlyOrganisedGenius]

This video really grinds my nothing

[@whynottalklikeapirat]

song title in there somewhere ...

[@choco_jack7016]

how do you not have gears?

[@ardinchesters128]

Sounds like a YIAY submission

[@ichaukan]

One more plane and it would totally grind my gears.

[@nootums]

@@ardinchesters128 hey! My man!

[@isaaccummings]

My grandpa had one of these, labeled as the "Politician Machine", because it went round and round doing nothing.

[@full-timepog6844]

Very much relevant still

[@DraconicDuelist]

Topical!

[@mihailmilev9909]

Yes very accurate

[@l4ffingdogg233]

😂

[@usualunusualkid7149]

based

[@MichaelHokefromCO]

My father wanted to have real elliptical arches in the house my parents built, so he made a large nothing-grinder jig the framers could use to construct the arches. It worked beautifully.

[@mansardmanor3869]

*As a custom house builder* I too use it for in-situ arches

[@mihailmilev9909]

@@mansardmanor3869 lol

[@mikem.a.253]

I wish my childhood teachers had shown half the love and passion for knowledge that you do. Thanks for your work!

[@Unpopular_0pinion]

Omg I know! I love how much he enjoys and appreciates what he talks about

[@bayatbayat9289]

0

[@sachimi_ggz]

First wish a good pay to teachers.

[@robertheller4583]

Me too, my childhood teacher just molested me

[@Rexvivor]

@@robertheller4583 weird flex but okay

[@drygordspellweaver8761]

The relationship between circles and triangles is one of the most fascinating. Enemies on the surface but secret lovers behind the curtains

[@mackenziegreenwood9197]

Most underrated comment right here

[@morgankosokowsky812]

^^^

[@DaBeezKneez]

Wtf.. lol

[@PC_Simo]

Also; in the Religion I follow, called: ”Cabtism”, started by my Best Friend, who is The Prophet, in the Religion; both circle and triangle are the symbols of anger. Though, in another, pagan religion I used to follow, before Cabtism, circle was the symbol of joy, and only triangle was the symbol of anger. **Side-note:** Square was the symbol of reason, in that pagan religion (Krasnian Paganism); and it’s the symbol of joy, in Cabtism. 🔴🔺🟥

[@videoinformer]

I love the camaraderie among various KZbin channels that share common or related interests. It always warms my heart when you mention each other in connection with each of your own work. I feel we are all sharing an experience together in that you enjoy watching each other and aren't just producers, but also viewers like me.

[@TheXenoEnder]

"So let me inflict some really beautiful and surprising explanations on you..." He makes me feel like a mathochist

[@TheMartinChronicles]

Badum bum.😄

[@GeorgeCowsert]

Ya know, Nothing Grinders can be useful for having an array of buttons that are only supposed to have one on at a time, like a special kind of dial.

[@Akira-nw4jl]

the way he presents this contraption with his Germanic accent, he sounds like he could take over the world with this. I love his enthusiasm! I wish my school grade teachers showed such interest in what they taught instead of watching the countdown to their retirement.

[@Artaxo]

10:20 Almost fell from my chair.

[@Mathologer]

Have to do this more often then :)

[@TheMrvidfreak]

Now get your BUTT back to the chair!

[@U014B]

I know how you feel. I'm always excited by a nice big BUT.

[@RadioJonophone]

Wake up at the back!

[@captainbodyshot2839]

he used force

[@danw1955]

Anyone here own a Spirograph as a kid? Most fun I ever had with drawing, since I can barely draw a straight line. A box of colored pens, a pack of 8 1/2 x 11 paper, and a Spirograph, and I could decorate my entire bedroom in a day (until my Mom got tired of having to buy a pack of paper every time she wanted to type a letter).🤣

[@CzKaa]

YES! Back in time (50 years) for me. :)

[@BradleyJustinGreen]

Yes I did, this video totally brought those memories to mind for me as well!

[@SteakCutFries]

This was my favorite thing to do when I would be at my grandparents house, after I found my mom's original set from the late 1960s. And now I've bought little travel sets for my own kids

[@bobbofly]

best x-mas gift I ever got! :))))))

[@SacredMilkOG]

Didn't know they were so old, pardon. But yeah I had one as a kid too. Lol

[@vegasprof5624]

At the age of 10, I was inspired to be a mathematician by two "popular" math books. Videos like this are quite entertaining to every curious person, and will inspire a new generation of budding mathematicians. Keep up the good work!

[@michaelbauers8800]

What books?

[@slook7094]

The Nothing Grinder? I've never heard it called that. I've always known it as the hillbilly entertainment center.

[@Mathologer]

Another fun name to add to my collection :)

[@mike62mcmanus]

I always thought it meant Joe "The" Grinder, the reason for many a divorce.

[@melone3631]

Same

[@melone3631]

Heard it from vsauce

[@TestTest-nv1dc]

Ive always thought of it as a bullshit grinder

[@TheJAMF]

2:05 For the puzzle: The blue ellipse is unique and every point further out produces an ellipse more resembling a circle, but never actually becoming one.

[@LucianoRobino]

are you sure that you don't get a similar elipse inside the circles, but rotated at 90°?

[@TheJAMF]

​@@LucianoRobino No, you have two points fixed (foci) on the horizontal for all the ellipses. No matter how long you make the arm, these two points stay fixed.

[@LucianoRobino]

@@TheJAMF wait, if you have 2 foci, that means you won't be able to get a circle, since that would means the foci collapse into each other, and having fixed foci won't allow it. Either way, regardless if in wrong, I still want to understand what happens to the points inside the circle, do they describe any figure?

[@TheJAMF]

@@LucianoRobino Well, the smaller you go (like inside the green ellipse), the flatter the ellipse will get.

[@BusinessVoid]

I built this in highschool. The final in woodshop was to make a wooden mechanism of some kind. We had 3 months to make it. My thought process was a strange engine thing. It was a very addicting fidget spinner before they existed. I had no idea I was literally copying a thing a famous philosopher made. My math nerd friend told me about the little machine I made. so now I'm here. It's the "your smart David." I needed today.

[@VIM365]

You’re* Lol, you goin on about how smart you are but make a 1st grade grammar mistake. You need some humility m8. Also I don’t believe you, not because this is incredibly difficult, it reality it’s not complex, but because you’re tryna come across as a genius, and I don’t believe that.

[@knut3hundra649]

@@VIM365 Bruh, who are you, chill down.

[@VIM365]

DJ KHALED people with huge egos strike a nerve

[@BusinessVoid]

@@VIM365 I'm not sure who you think I am, but spelling has never been my strong suit. What was happening was that that whole week was just failure after failure. Having a friend over to break quarantine was a nice change of pace. We went over some old nick-knack stuff I had on the shelf. He thought I bought it somewhere, till he saw my name on the bottom. if your goal was to make a depressed person sadder than you did your job. As for ego, I wish I had such confidence. you may make accusations biased on what little interactions we make. You may have your own convictions but others have feelings.

[@VIM365]

David Diaz you know what? My bad dude. Sorry for being so harsh.

[@KSignalEingang]

Just got myself a 3D printer (a Creality Ender 3 Pro, highly recommended if you're looking for an entry-level printer), so naturally I had to come back to this video & grab the SLTs. It's the first build I've attempted that involved moving parts and it came out pretty well! I built the two-slider version, scaled down 77% to save on time/materials. Had to glue the pegs into the sliders as they wouldn't lock (possibly due to the downscaling) but that was easy enough to do, and the result performs flawlessly. Grinds all the nothing I could ever want. It was fun being able to show the kids this video with the actual grinder there for them to play with. Now they're bugging me to build the rest of the set... Well, if I must!

[@xnick_uy]

This video is extremely well done! I love the animations and the 3D printer stuff.

[@Mathologer]

:)

[@barakdeathsong4265]

:) :) :))))))))))))))))))))))))))))) Guess which is me. Go on.

[@pinballrobbie]

Used that device at work making elliptical coffee tables with the aid of a small woodwork router, very useful device. Way better than two nails and a loop of string. Great video bye the way.

[@andrewroberts5988]

This video is a true masterpiece. Revealing the way the nothing grinder can have many axes that won't bump into each other was so well done. Excellent video and demonstration.

[@AleMalave92]

Watching this makes me wish that I had a teacher like you when I was in school!

[@unvergebeneid]

Oh my, your t-shirts always crack me up soooo much 😂

[@AaronRogge]

Love the t-shirt. I want one :)

[@GregorShapiro]

@@AaronRogge www.redbubble.com/people/theshirtyurt/works/24693541-math-puns-first-sine-of-madness?p=t-shirt&style=mens

[@nacoran]

Angle jokes? Don't be obtuse. Wait until at least he has acute one, right?

[@victorcroasdale4992]

@@nacoran I went off on a tangent cos of reading his T shirt.

[@yummyfruitsuace993]

youre're*

[@psy7251]

As usual, one of the best videos on KZbin. Thank you, especially when showing that the locus of any point on the smaller circle of radius r rolling inside the larger circle of radius 2r is a straight line. I've taught high school mathematics for almost 20 years and didn't realize that. Beautifully explained!

[@jafo4775]

We used to slot two boards, set them perpendicular, and with another board (with two spaced nails riding in the grooves) create any size ellipse for window or door headers. Worked better than the string and two nail method. Thanks for the vid.

[@PRH123]

I like very much the mix of history, mechanics, and mathematics. You have a very good style of delivery as well. I don’t have a math brain and am always thinking as you speak and demonstrate that this is interesting and important, but I don’t get all of the significance, but I want to keep watching. Hopefully some of it will get through my thick head. Good work!

[@groovinhooves]

Come now, dear Mathologer, ellipses are not 'squished' circles, they are foreshortened views of circles from angles declined from the perpendicular. Stop pretending that space just bends like that :D

[@ratsass7201]

Exactly!

[@sethryclaus]

That's your reaction. Mine was, "thank god he isn't talking about conic sections". Your comment made me laugh though, thanks :)

[@animationtime7265]

It's just a simple way say it. Get of your high horse.

[@Sivanot]

@@animationtime7265 and this was pretty obviously a joke, albeit a true one, chill.

[@rivercritter533]

A man of wisdom

[@TheScienceBiome]

I love how you present everything!

[@doctormarcelopizarro4012]

I loved math in school, then I became a Medical Doctor to apply the art of abstraction, now I still enjoy math and logic like in my childhood. I love your channel, keep doing this forever

[@rogerg_zapata]

Although I'm not good at maths, I like when the concepts, like the one presented in this video, become so clear, at the point that I can understand (I'm still lost with many things, though) and enjoy the beauty of maths! Thanks for sharing the video!

[@RammusTheArmordillo]

7:36 "Yep, it's spirograph time" 😂😂

[@MookalH]

Donald Piniach what

[@carlweiser1319]

Drinking game, take a shot each time he says "neat huh?"

[@the1gip]

I don't know what's more lovely, your explanations or your mesmerising voice. Your delivery is utterly exquisite.

[@Bordpie]

You can also make a little gear ratio out of this mechanism. If you take the entire animation of the Tusi couple e.g. the one right at the end of the video, and rotate it clockwise about the centre of the large circle, and at the same angular speed the small circle is rolling around the big circle, then the small circle will stop moving around the large circle and rotate on the spot. The large circle will also rotate about its centre, but at half the angular speed of the small circle. Therefore, if you attach an axle to the centre of the small circle and an axle to the centre of the large circle you can make a 2:1 gear ratio just using straight slots and pins. The limitations to this mechanism is that the output shaft must be on the opposite side of the 'gears' to the input shaft. Somewhere on youtube there is a video of this gear mechanism someone made from wood I think but I can't find it. It still really fascinates me that you can make a perfect gear ratio just using this simple geometry of straight slots and pins, whereas normal gears require a much more complex geometric shape. I have a 3D printer and will print out your design :). This also really makes me want to make this gear mechanism and print it off (it's something I've been thinking about for a while). I could even make it in OpenSCAD and make it parametric, so you can use any number of pins and show that the Tusi couple will work.

[@litigioussociety4249]

It's really weird how focus of the eyes affects the dots. Focus on one dot, and the linear motion is obvious, but when not focusing on any specific dot, then the circular motion of all the dots becomes obvious.

[@Mathologer]

Yes, its a great effect :)

[@williamchamberlain2263]

Fish vs tiger, maybe; focus on catching one fish in a school, but put together lots of little movements to spot the tiger. Failing the former leaves you hungry, but failing the latter leaves you never hungry again.

[@DemPilafian]

So you can try it as many times as you like: 4:46

[@MAGnetICus_Attractus]

I was thinking different color dots in flash would be a trip. Transitions from one color to another as it travels across the line.

[@frenchfriar]

My father used to make these in his woodshop, he called his "smoke grinders".

[@Jason-bd5iq]

This is one of the most beautiful things I’ve ever seen in my life.

[@DEATH_TO_TYRANTS]

KZbin recommend this to me, and boy am I glad they did. Thanks for the video. I look forward too more.

[@brendanmorris4794]

I love your videos. So much knowledge packed in an enjoyable, humorous package! Keep up the good work!

[@AlejandroBravo0]

Man, I really love your videos. Thanks for your work, honestly.

[@ketongu]

man, that proof at the end was cool. an example of ostensibly difficult maths being broken down into fun, easy to understand fundamentals.

[@MrCrashDavi]

+

[@TransSappho]

I’m a geophysical sciences major who honestly resented most of the math I’ve been required to take to pursue paleontology, but the videos on this channel are made with such excitement and fun that I can easily engage with this subject matter

[@dominikorlowski3059]

That is awesome that you made and provide those print files. Hats off Sir.

[@enysuntra1347]

5:17 it's pronounced "ad-Din at-Tusi" - solar and lunar letters. The "al"-consonant doubles the 1st consonant for some consonants. That's how "Salah al-Din" became "Saladin" latinised. If you transliterate phonetically, you'll see him as "Salah ad-Din". "al-Gibr" stays so, "algebra".

[@mstech-gamingandmore1827]

indeed

[@2adamast]

Supposing prononciation was unchanged over 800 years and shared through ethnicities

[@enysuntra1347]

@@2adamast surprisingly few changes. "Moon" and "Sun" consonants didn't change in High Arabian, although they aren't used now colloquially.

[@MrTiti]

this contradicts itself

[@MrTiti]

because it disappears instead of doubling

[@gregorcutt1199]

Wow, I like this guy's presentation so much. The KZbin trend is towards more yelling, hyperbole, "excitement"

[@jimmysuperchannel1527]

Hyperbole, hyperbola

[@taysem321]

He sounds like he is bored

[@jordanr6639]

This video gives very concise examples of how nothing can really be something to the creative thinker. Where nothing previously existed there are now a host of fresh examples of trigonometry and how the modern day circle can be adjusted to become an ellipse simply by adding an 'a' into the equation. This guy is a greats maths teacher.

[@avshiloh2438]

Burkhardt, your love and enthusiasm for math and logic shine through vividly. THANK YOU!!!

[@roycsinclair]

When I saw this I thought of the Spirograph toy which is essentially the same.

[@SteveFrenchWoodNStuff]

Excellent explanation. Thanks!

[@Mathologer]

Have not heard from you for a while. How are things going? These nothing grinders also make excellent woodworking projects. Maybe something for you to tackle? I've never seen a three+ slider one done in wood. Someone also pointed out that people still use the nothing grinder idea to cut ellipses using a router. Have to check this out too :)

[@thesnakednake]

This is one of your best videos yet, to be honest. I really liked the visuals in this one

[@Zyvo2]

I wish you were my math teacher. This is far more interesting and applicative than the bs they taught me in school.

[@DanBurgaud]

7:30 Suddenly I saw a toy I played back when I was in Grade School!

[@maza8041]

I think it's a possibility to turn this "Nothing grinder" into a working engine...

[@lil0of]

it's the rotary engine's less successful brother

[@justanotherjosh6284]

10 second into this i was thinking the same thing. i feel a compression engine would benefit the most

[@bradleyweiss1089]

JoshTheKid You are thinking of a radial airplane engine.

[@CrispyChicken38]

The gear for a hand crank power generator

[@bryceforsyth8521]

@@lil0of I think you mean Wankel.

[@mrtwister1775]

I'm not into all the math equations and such, but you really do make it interesting. I wish I had you as a math teacher.

[@Amb3rjack]

What a completely fantastic video! Utterly amazing! Subscribed straight away.

[@carlosmejia5728]

Just one word: BEATIFUL!... Isn't just wonderful we live in a Universe that has all this physical properties??... I never get tired of watching your presentations... 😎

[@unknownnepali772]

THE BEAUTY OF "MATHEMATICS" ♥

[@NuYiDao]

Thanks, suitably devastated. Please bring more.

[@Gafa996Gaddisa]

I am waiting the next excitement &educational video of @Mathologer. Always with his nice sense of humor.

[@jimbeam992]

So is the rotary engine a complex "do-nothing" machine? Can you verify or am I just over thinking the Mazda power plant?

[@CSkwirl]

3:00 I was also immediately thinking you could make a compact 6 cylinder 2-stroke with the crank/pto at the front and exhaust at the rear centre...it's probably already been done

[@tylerdurden3722]

I was thinking the same. I wonder if a radial engine is also a nothing grinder...a simple one.

[@makismakiavelis5718]

Nah, to me it looks more like a radial aircraft engine.

[@pepe6666]

you guys got it all wrong. you want a 1024 cylinder engine

[@Cole-ek7fh]

Jim Beam the wankel is different becaue of internal combustion.

[@thefuzzman]

Damn, I thought this was about a weed grinder, but left with knowledge. Amazing video!

[@EmeraldLavigne]

Learning math is so cool, lol

[@crhu319]

It won't grind weed but watching it will save on weed

[@thefuzzman]

@@crhu319 actually I wanted to smoke more watching this due to it being so cool lol

[@lightspiritblix1423]

I 3-D printed the hexagon nothing grinder you provided, and the print worked perfectly first try. I have a Creality Ender 3, and it’s by far the coolest thing I’ve printed from the Internet. Thanks!

[@Mathologer]

Great :)

[@glenntaylor1613]

Love the shirt and your humorous approach.

[@tombouie]

Holy crap, I'm a retired military physicist & I never got such a competent/complete explanation for a math guy. I guess you math guys ain't all bad afterall. Thks PS: Typically when a KZbinr rrrrreally impresses me. Just for fun, I go outside & humbly bow to them in their general direction. ?Where about do you live?

[@Mathologer]

Glad you like the video so much. Melbourne :) What sort of things did you work on as a military physicist?

[@tombouie]

​@@Mathologer Oh the usual lasers, bombs, satellites, fix the colonel's computer, etc, etc. Trying to find good academics that'll provide competent & complete solutions/designs is extremely difficult. It seems most of them expect the-world to somehow conform to their magic PhD math. Here's some of my experience dealing with academics (OCC The Skeptical Caveman Ep #0 "Pilot" kzbin.info/www/bejne/nWK7YnmFj9KgjKM ). You might want to try to do some consulting work for aussie military research faculities via their main research contractors. Be sure to point them to your KZbin channel. Oh, I'll calculate a vector from the US to Melbourne & do my humble bow towards Melbourne tomorrow morning. Thks PS: Hmmmmm, now I have to watch all your videos. A geek's work is never done.

[@Mathologer]

​@@tombouie :)

[@tombouie]

@Matrix29bear Hmmm, I'm retired/clueless on common core stuff but you might be interested in these: The College Meltdown @CrushTheStreet kzbin.info/www/bejne/pJTUq6F8oqaho80 Default: the Student Loan Documentary (Broadcast Version) kzbin.info/www/bejne/rae0g2xpeJuhaKc How college loans exploit students for profit | Sajay Samuel kzbin.info/www/bejne/j4m6fKiBYramq5Y For these college students, the most difficult test may be basic survival kzbin.info/www/bejne/bHPNp32Pf8qpjM0 Elon Musk, Jay Z, Warren Buffett, and other's criticism on college kzbin.info/www/bejne/rpqbdYacnNimY5o The Reset Button: The Great Fantasy of Academia | Brian Harrington | TEDxUTSC kzbin.info/www/bejne/eKellXtrdrCfhMU The Truth About PhD Unemployment Data kzbin.info/www/bejne/fKXQkmWEmZitobM The Biggest Scam in America kzbin.info/www/bejne/qonKdHprZb6ijdU Ferengi Rules of Acquisition kzbin.info/www/bejne/hqepinWhmtikfbc 6 Problems with our School System kzbin.info/www/bejne/pZzTmGCii7x_mKc Why I Hate School kzbin.info/www/bejne/mIGXio2kppmihKM How School Makes Kids Less Intelligent | Eddy Zhong | TEDxYouth@BeaconStreet kzbin.info/www/bejne/aIrXZ6WXn5KGZ68&vl=en How School Prepared You To Fail kzbin.info/www/bejne/mqmzh62aiZaffZI Do schools kill creativity? | Sir Ken Robinson kzbin.info/www/bejne/n3icdHhratyVqrs Humans Need Not Apply kzbin.info/www/bejne/bYHUXoZrapyLh7c The Rise of the Machines - Why Automation is Different this Time kzbin.info/www/bejne/jYSummt-m8ire80

[@EatMyYeeties]

@Matrix29bear Trust me, common core isnt deterring people from getting into math. I hated the program and how simple it was in high school, so I just taught myself more advanced math. I'm 23.

[@szekelybalazs8803]

"Typical mathematical denial of reality." :)

[@aidanm8954]

Ngl I'd want this guy to teach my math class, he's so straight forward and explains things so well.

[@JosephElfassi]

Just love this channel.

[@Demki]

2:05 Going by intuition alone (haven't proven it), I'm going to say 3 points: 2 of them will be symmetrically positioned between the points that move on straight lines, drawing ellipses "perpendicular" to one another, which is the same shape rotated, and a third point will draw a scaled up version of that ellipse and will be on the "long side" side of the arm. All this except for the degenerate cases: A circle has 1 point on the arm that draws it (or 2 if you consider the point at infinity which again by intuition likely draws a circle), and a line (a degenerate "infinitely stretched out" ellipse) has 2 points that draw it. (If the arm would be extended in both directions, change that 3 to a 4) edit: Now that I've reached 7:05, it feels like my intuition was correct.

[@Mathologer]

Very good :)

[@awfullufwa]

Sorry for the year late reply. Ya know, I used to be pretty good at maths in high school a quarter century ago so when Mathologer popped a quiz I decided to pause the vid and take it. I closed my eyes and tried to envision it (just a thing I do when trying to concentrate, helps me remove other stimuli). I saw ellipses squishing down to a line. But I think I somehow saw them opening up again into what I questioned might be another circle (the point at infinity which would draw another circle, as you mentioned). Idk, still trying to visualize how they would plot. In my 40's now so I'm kinda old and used spirographs as a kid, they were very common toys. I suspected the ellipses would rotate somehow but I wasn't quite on the money there. You said they'd be perpendicular. That means just two sets of ellipses. Am I getting this right? Wasn't sure how to count the points either but I think you connected some dots for me. And then I watched through the rest of the vid and it all came together. I spent a year in college back in the day but wasn't sure what I wanted so I just quit and joined the workforce. Lately I've been wanting to go back and earn a degree in... something. Think I might now research a path in mathematics as it pertains to my career in Aerospace Machining. Sorry for the long post, this just really stirred something in me. Or maybe I'm just a total layman who should keep his nose outta things he only thinks he understands. Meh, and this is why I never go back to school. The crushing doubt.

[@jaybruh4u]

My grandpa made one of these for me! He called it a BS grinder 😂

[@richtigmann1]

a blue shape grinder?

[@youtubecensors5419]

Mine too! Forgot all about it. He made it in the 70's.

[@ayubshaikh9156]

Beautifully illustrated....... With passion

[@rez194]

the best teachers teach from the heart. i enjoyed watching

[@rezamiau]

5:15 Khajeh Nasir Al-din-e Tousi [NOT Al-Tousi], was Great Iranian astronomer and also mathematician. he was from Tous, a city in North-east of iran.

[@ramirmanlavi5768]

"Of course you wont be able to sleep tonight when you dont know the answer" H E ' S R E A D I N G M Y T H O U G H T S

[@SwedeEad]

I've been meaning to make one of these for ages after watching a woodworker on KZbin use one to cut ellipses from sheet material to make table tops. He attached a router to the end of the arm. I thought it was magical at the time. I've never heard of it referred to as a 'do nothing machine' it definitely does something. If my school teachers were half as good at clear explanations as you, I'd probably have taken a different path in life. But I'm still warm and still breathing so it's never too late! Thanks and subscribed.

[@TyCetto]

Math is King! Loved it!

[@LanceThumping]

The final proof seems unnecessary except to just provide additional assurance that the arcs are the same length because whenever something rolls without slipping it necessarily is tracing the same arc.

[@felixruben4955]

NerdyPi , true. Also the lenghts of the circles don‘t change over time.

[@trogdorstrngbd]

Not the point (pun not intended). If the smaller circle had, say, 1/3 the diameter of the larger one, it would of course still be true that traced arcs have the same length, but the point being tracked won't trace a line. The final step of the proof involving the parallel lines only works when the diameter ratio is 1/2.

[@Ucceah]

i'll have to strongly object to one point: while "milage may vary", it's not so much depending on the printer (as long as it's construction is adequate), but much more so on the operators abilities to tune the machine, and dial in the right slicer settings for any given print and material! a $2000 machine might be able to get the job done a little faster*, but in terms of print quality, it's got no siginificant edge on a $300 budget machine. ( *= without a detrement to the print's visual quality, )

[@aterack833]

Cuda FX and here I am wanting to build a tower style reprap printer with a dual pivot arm and 1 motor 2 solenoids and 3 encoders

[@rexcadral3468]

Wonderful demonstration.

[@YodaWhat]

Really beautiful graphic animations! Mesmerizing, and inspiring.

[@MisterIncog]

About green and red angles: there's a basic theorem: inscribed angle equals half the arc it intercepts and central angle equals the arc it intercepts. And you just prove it again for idk six-graders (no offense to six-graders).

[@alarageref2481]

I think all ellipses are drawn three times. If the arm approaches infinity, the outer point will trace a circle. The first pivot point traces a line. As discussed, a point between the two pivots traces a circle, and the second pivot also traces a line. Therefore we have a continuous transition from circle -> line -> circle -> line. Each segment of the transition will contain ellipses of all eccentricities exactly once.

[@Mathologer]

That's it, but there are some interesting exceptions (the extreme cases :)

[@alarageref2481]

Mathologer ahh there are two circles and two lines only. Mathematicians never miss an opportunity for pedantry :P

[@inyobill]

@@alarageref2481 One man's pedantry is another's precision.

[@bentonpix]

The outer point on the arm can never trace a circle no matter how long it is. There's no such thing as "approaching infinity".

[@inyobill]

@@bentonpix Where did you get your Maths degree? This is an informal forum, and there is no ambiguity in the meaning.

[@doordieace5high]

Subscribed. Glad I found your channel. So much better than most of the stuff on KZbin.

[@vaidik03]

Amazing video and your explanation was beyond any other...Thanks :)

[@cdw3423]

I don't know why people this this is a do nothing machine. People still use this design with a router to cut out an ellipse.

[@Mathologer]

Thanks for pointing this out. Here is a video of someone demonstrating how this is done kzbin.info/www/bejne/kHuTaouGpqeLaJo :)

[@satibel]

I'd say there's 2 other ellipse, one between the red and green, and another between the red and the center, rotated 90 degrees.

[@markmandel6738]

There's an infinite number of ellipses, as there's an infinite number of points on the (axis of the) grinder handle: the infinity of real numbers.

[@errollbrantley]

This is so informative and useful. Thank you

[@ogretowman]

Math past algebra was hard for me , but if I would have had an instructor like you it probably would not have been ! Cool presentation and a new sub too ! Thank you

[@TheClimbingBronyOldColt]

Schools: We will teach you to hate math! This video: Math, is actually fascinating!

[@agod5608]

The internet, the world's largest library club.

[@gregsmith7828]

it could be used to rive pistons or a well pump

[@Mathologer]

Here is a video of someone using this idea to cut an ellipse with a router kzbin.info/www/bejne/kHuTaouGpqeLaJo :)

[@swarfmonster3998]

Great video, really enjoyed it!

[@kk-lr5ud]

And once again! The day is saved! Thanks to MATHOLOGER MAN!!!

[@DeFaulty101]

As the arm's length approaches infinity (relative to the distance between the pegs), I imagine the oval produced would approach perfect circle-shape.

[@inyobill]

Holding the distance between the pivots (P) constant, as the arm (A) -> ∞, P/A -> 0. Or, Lim A -> ∞, P/A = 0.

[@AlanKlughammer]

Or, since the eclipse is getting more and more "squished" it will trace a line.... Think about that for a while...

[@inyobill]

@@AlanKlughammer Look at the illustration at 1:31. It is clear that ellipses further from the center have lower eccentricty.

[@AlanKlughammer]

@@inyobill Yes you are correct, I was just going by his statement of squishing the eclipse. The illustration you reference actually shows the Mathologer is a bit misleading. The circle is only at the interior of the pegs, Once you get past the distance of the outer peg, the ellipsis get less and less squished.

[@inyobill]

@@AlanKlughammer Thanks for the kind reply. Entirely possible I had misunderstood. Especially when there's something I don't understand, I post a statement to try to elicit a response to try to figure out where I'm wrong, and somewhat more rarely, correct.

[@evaristegalois6282]

*Évariste Galois approves*

[@burklander3338]

Thank you for a wonderful use of my time. I learned something, I heard a mesmerizing voice, I watched science in action. I subscribed to your channel. Thanks again.

[@danylipsker]

Excellent explanation, thanks a lot

[@wkrijthe]

You may call them nothing grinders, but they actually show how combustion engines work. I wouldn't call that nothing.

[@RR67890]

Can't say as I agree with that statement. It's only sliders, no intake, compression, ignition, exhaust. It's only similar because there is a crankshaft, but it acts nothing like an internal combustion engine. So it's nothing.

[@wkrijthe]

@@RR67890 I could say you're nitpicking, but maybe a better term would be piston engine.

[@FireyDeath4]

Fled when he begun to do the trigonometry.

[@kallewirsch2263]

Why? Trigonometry often is pretty easy, when you get the hang of it. Almost always you search for special triangles. The first thing you always do is looking if there is one right trinagle somewhere. Always! Because if you find one, then almost always the rest becomes a piece of cake. Phythagoras paired with the definitions of sine of cosine (but most often Phythagoras alone) safes the day. If you cannot find a right triangle, then look out for isoceles triangles. Why? Because there is one thing we know for sure: the sum of all angles in a triangle adds up to 180. So even if you do not know the values of the angles, you do know that 2 of them must be equal. Which often enables you to use the "Z-trick" to transfer that angle to some other angle in the drawing and continue working from there. But the most important thing of all is: Make a drawing! This cannot be emphasized enough. Make a scetch! Label what you do know and what you want to know. Then continue with searching (and finding) the right triangle :-)

[@lawrencedoliveiro9104]

/me pulls string on Talking Barbie Doll “Math is hard!” Moral: don’t get life lessons from a Talking Barbie Doll.

[@rich7787]

What an excellent video, Bravo!

[@sayochikun3288]

perfect explanation and examples

[@mr.insectoid]

Что я тут делаю?! Почему это у меня в рекомендациях?! Но это круто, соглашусь

[@lppunto]

Like if you've been waiting for this since Thinkercon.

[@Mathologer]

Did you actually watch me talk about this stuff there? :)

[@ra7orblade]

I enjoyed this WAAAAY more than I dare admit

[@mike62mcmanus]

Your easy to listen to, this helps me relax and sleep.... Thank you so much.