One more plane and it would totally grind my gears.
@nootums
5 жыл бұрын
@@ardinchesters128 hey! My man!
@mikem.a.253
5 жыл бұрын
I wish my childhood teachers had shown half the love and passion for knowledge that you do. Thanks for your work!
@Unpopular_0pinion
4 жыл бұрын
Omg I know! I love how much he enjoys and appreciates what he talks about
@bayatbayat9289
4 жыл бұрын
0
@sachimi_ggz
4 жыл бұрын
First wish a good pay to teachers.
@robertheller4583
4 жыл бұрын
Me too, my childhood teacher just molested me
@Rexvivor
4 жыл бұрын
@@robertheller4583 weird flex but okay
@isaaccummings
3 жыл бұрын
My grandpa had one of these, labeled as the "Politician Machine", because it went round and round doing nothing.
@full-timepog6844
3 жыл бұрын
Very much relevant still
@DraconicDuelist
3 жыл бұрын
Topical!
@mihailmilev9909
3 жыл бұрын
Yes very accurate
@l4ffingdogg233
3 жыл бұрын
😂
@usualunusualkid7149
3 жыл бұрын
based
@MichaelHokefromCO
5 жыл бұрын
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
3 жыл бұрын
*As a custom house builder* I too use it for in-situ arches
@mihailmilev9909
3 жыл бұрын
@@mansardmanor3869 lol
@slook7094
5 жыл бұрын
The Nothing Grinder? I've never heard it called that. I've always known it as the hillbilly entertainment center.
@Mathologer
5 жыл бұрын
Another fun name to add to my collection :)
@melone3631
4 жыл бұрын
Same
@melone3631
4 жыл бұрын
Heard it from vsauce
@TestTest-nv1dc
4 жыл бұрын
Ive always thought of it as a bullshit grinder
@1pcfred
3 жыл бұрын
When I was first introduced to the idea the name of it was, "a do nothing machine".
@groovinhooves
4 жыл бұрын
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
4 жыл бұрын
Exactly!
@sethryclaus
4 жыл бұрын
That's your reaction. Mine was, "thank god he isn't talking about conic sections". Your comment made me laugh though, thanks :)
@animationtime7265
4 жыл бұрын
It's just a simple way say it. Get of your high horse.
@Sivanot
4 жыл бұрын
@@animationtime7265 and this was pretty obviously a joke, albeit a true one, chill.
@rivercritter533
4 жыл бұрын
A man of wisdom
@Artaxo
5 жыл бұрын
10:20 Almost fell from my chair.
@Mathologer
5 жыл бұрын
Have to do this more often then :)
@TheMrvidfreak
5 жыл бұрын
Now get your BUTT back to the chair!
@U014B
5 жыл бұрын
I know how you feel. I'm always excited by a nice big BUT.
@RadioJonophone
5 жыл бұрын
Wake up at the back!
@captainbodyshot2839
5 жыл бұрын
he used force
@TheXenoEnder
3 жыл бұрын
"So let me inflict some really beautiful and surprising explanations on you..." He makes me feel like a mathochist
@TheMartinChronicles
3 жыл бұрын
Badum bum.😄
@danw1955
3 жыл бұрын
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
3 жыл бұрын
YES! Back in time (50 years) for me. :)
@BradleyJustinGreen
3 жыл бұрын
Yes I did, this video totally brought those memories to mind for me as well!
@SteakCutFries
3 жыл бұрын
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
3 жыл бұрын
best x-mas gift I ever got! :))))))
@SacredMilkOG
3 жыл бұрын
Didn't know they were so old, pardon. But yeah I had one as a kid too. Lol
@drygordspellweaver8761
3 жыл бұрын
The relationship between circles and triangles is one of the most fascinating. Enemies on the surface but secret lovers behind the curtains
@mackenziegreenwood9197
3 жыл бұрын
Most underrated comment right here
@morgankosokowsky812
3 жыл бұрын
^^^
@DaBeezKneez
3 жыл бұрын
Wtf.. lol
@PC_Simo
10 ай бұрын
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. 🔴🔺🟥
@GeorgeCowsert
5 жыл бұрын
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.
@TheJAMF
3 жыл бұрын
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
Жыл бұрын
are you sure that you don't get a similar elipse inside the circles, but rotated at 90°?
@TheJAMF
Жыл бұрын
@@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
Жыл бұрын
@@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
Жыл бұрын
@@LucianoRobino Well, the smaller you go (like inside the green ellipse), the flatter the ellipse will get.
@videoinformer
5 жыл бұрын
I love the camaraderie among various KZitem 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.
@PRH123
3 жыл бұрын
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!
@xnick_uy
5 жыл бұрын
This video is extremely well done! I love the animations and the 3D printer stuff.
@Mathologer
5 жыл бұрын
:)
@barakdeathsong4265
5 жыл бұрын
:) :) :))))))))))))))))))))))))))))) Guess which is me. Go on.
@jimbeam992
5 жыл бұрын
So is the rotary engine a complex "do-nothing" machine? Can you verify or am I just over thinking the Mazda power plant?
@CSkwirl
5 жыл бұрын
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
5 жыл бұрын
I was thinking the same. I wonder if a radial engine is also a nothing grinder...a simple one.
@makismakiavelis5718
5 жыл бұрын
Nah, to me it looks more like a radial aircraft engine.
@pepe6666
5 жыл бұрын
you guys got it all wrong. you want a 1024 cylinder engine
@Cole-ek7fh
5 жыл бұрын
Jim Beam the wankel is different becaue of internal combustion.
@szekelybalazs8803
5 жыл бұрын
"Typical mathematical denial of reality." :)
@KSignalEingang
4 жыл бұрын
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!
@unvergebeneid
5 жыл бұрын
Oh my, your t-shirts always crack me up soooo much 😂
Angle jokes? Don't be obtuse. Wait until at least he has acute one, right?
@victorcroasdale4992
5 жыл бұрын
@@nacoran I went off on a tangent cos of reading his T shirt.
@yummyfruitsuace993
5 жыл бұрын
youre're*
@maza8041
4 жыл бұрын
I think it's a possibility to turn this "Nothing grinder" into a working engine...
@lil0of
4 жыл бұрын
it's the rotary engine's less successful brother
@justanotherjosh6284
4 жыл бұрын
10 second into this i was thinking the same thing. i feel a compression engine would benefit the most
@bradleyweiss1089
4 жыл бұрын
JoshTheKid You are thinking of a radial airplane engine.
@CrispyChicken38
4 жыл бұрын
The gear for a hand crank power generator
@bryceforsyth8521
3 жыл бұрын
@@lil0of I think you mean Wankel.
@enysuntra1347
5 жыл бұрын
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
4 жыл бұрын
indeed
@2adamast
3 жыл бұрын
Supposing prononciation was unchanged over 800 years and shared through ethnicities
@enysuntra1347
3 жыл бұрын
@@2adamast surprisingly few changes. "Moon" and "Sun" consonants didn't change in High Arabian, although they aren't used now colloquially.
@MrTiti
3 жыл бұрын
this contradicts itself
@MrTiti
3 жыл бұрын
because it disappears instead of doubling
@Akira-nw4jl
5 жыл бұрын
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.
@vegasprof5624
3 жыл бұрын
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
2 жыл бұрын
What books?
@pinballrobbie
4 жыл бұрын
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.
@BusinessVoid
4 жыл бұрын
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
4 жыл бұрын
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
4 жыл бұрын
@@VIM365 Bruh, who are you, chill down.
@VIM365
4 жыл бұрын
DJ KHALED people with huge egos strike a nerve
@BusinessVoid
4 жыл бұрын
@@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
4 жыл бұрын
David Diaz you know what? My bad dude. Sorry for being so harsh.
@carlweiser1319
4 жыл бұрын
Drinking game, take a shot each time he says "neat huh?"
@litigioussociety4249
5 жыл бұрын
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
5 жыл бұрын
Yes, its a great effect :)
@williamchamberlain2263
5 жыл бұрын
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
5 жыл бұрын
So you can try it as many times as you like: 4:46
@MAGnetICus_Attractus
5 жыл бұрын
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
4 жыл бұрын
My father used to make these in his woodshop, he called his "smoke grinders".
@AleMalave92
5 жыл бұрын
Watching this makes me wish that I had a teacher like you when I was in school!
@tombouie
5 жыл бұрын
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 KZitemr rrrrreally impresses me. Just for fun, I go outside & humbly bow to them in their general direction. ?Where about do you live?
@Mathologer
5 жыл бұрын
Glad you like the video so much. Melbourne :) What sort of things did you work on as a military physicist?
@tombouie
5 жыл бұрын
@@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" kzitem.info/news/bejne/yGeOl3qFk5-eiXY ). 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 KZitem 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
5 жыл бұрын
@@tombouie :)
@tombouie
5 жыл бұрын
@Matrix29bear Hmmm, I'm retired/clueless on common core stuff but you might be interested in these: The College Meltdown @CrushTheStreet kzitem.info/news/bejne/z5mn4KJ8pnOfoKA Default: the Student Loan Documentary (Broadcast Version) kzitem.info/news/bejne/2KyHuG1pfGifZXo How college loans exploit students for profit | Sajay Samuel kzitem.info/news/bejne/uo6NsamBZoOkqGk For these college students, the most difficult test may be basic survival kzitem.info/news/bejne/l3ig3H6Pg5eniaA Elon Musk, Jay Z, Warren Buffett, and other's criticism on college kzitem.info/news/bejne/2Z9uqoecoKWkYG0 The Reset Button: The Great Fantasy of Academia | Brian Harrington | TEDxUTSC kzitem.info/news/bejne/o6x4ynxren2dgZg The Truth About PhD Unemployment Data kzitem.info/news/bejne/p6qjx2aEnWWrnoY The Biggest Scam in America kzitem.info/news/bejne/1Y6dqXtraYugiqg Ferengi Rules of Acquisition kzitem.info/news/bejne/sax8v3ahnqWieoo 6 Problems with our School System kzitem.info/news/bejne/0KGmzWGij4l9lXo Why I Hate School kzitem.info/news/bejne/w4Zqv46kqmaggXY How School Makes Kids Less Intelligent | Eddy Zhong | TEDxYouth@BeaconStreet kzitem.info/news/bejne/k4-qnKaXo1-EZII&vl=en How School Prepared You To Fail kzitem.info/news/bejne/xa6GvK6ajWOdemU Do schools kill creativity? | Sir Ken Robinson kzitem.info/news/bejne/yn1vqXlrbqmTp44 Humans Need Not Apply kzitem.info/news/bejne/mIank4drbmmJhIo The Rise of the Machines - Why Automation is Different this Time kzitem.info/news/bejne/uImBz2x-n5WpeKA
@EatMyYeeties
5 жыл бұрын
@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.
@andrewroberts5988
3 жыл бұрын
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.
@RammusTheArmordillo
5 жыл бұрын
7:36 "Yep, it's spirograph time" 😂😂
@MookalH
4 жыл бұрын
Donald Piniach what
@gregorcutt1199
5 жыл бұрын
Wow, I like this guy's presentation so much. The KZitem trend is towards more yelling, hyperbole, "excitement"
@jimmysuperchannel1527
5 жыл бұрын
Hyperbole, hyperbola
@taysem321
5 жыл бұрын
He sounds like he is bored
@rezamiau
5 жыл бұрын
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.
@psy7251
4 жыл бұрын
As usual, one of the best videos on KZitem. 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!
@jaybruh4u
5 жыл бұрын
My grandpa made one of these for me! He called it a BS grinder 😂
@richtigmann1
5 жыл бұрын
a blue shape grinder?
@youtubecensors5419
5 жыл бұрын
Mine too! Forgot all about it. He made it in the 70's.
@roycsinclair
3 жыл бұрын
When I saw this I thought of the Spirograph toy which is essentially the same.
@ramirmanlavi5768
4 жыл бұрын
"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
@rogerg_zapata
5 жыл бұрын
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!
@DanBurgaud
4 жыл бұрын
7:30 Suddenly I saw a toy I played back when I was in Grade School!
@lawrencedoliveiro9104
3 жыл бұрын
5:17 One of the luminaries from the Islamic Golden Age, back when Europe was still in the Dark Ages.
@Bordpie
5 жыл бұрын
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.
@thefuzzman
4 жыл бұрын
Damn, I thought this was about a weed grinder, but left with knowledge. Amazing video!
@EmeraldLavigne
3 жыл бұрын
Learning math is so cool, lol
@crhu319
3 жыл бұрын
It won't grind weed but watching it will save on weed
@thefuzzman
3 жыл бұрын
@@crhu319 actually I wanted to smoke more watching this due to it being so cool lol
@AlejandroBravo0
5 жыл бұрын
Man, I really love your videos. Thanks for your work, honestly.
@wkrijthe
5 жыл бұрын
You may call them nothing grinders, but they actually show how combustion engines work. I wouldn't call that nothing.
@RR67890
5 жыл бұрын
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
5 жыл бұрын
@@RR67890 I could say you're nitpicking, but maybe a better term would be piston engine.
@cdw3423
5 жыл бұрын
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
5 жыл бұрын
Thanks for pointing this out. Here is a video of someone demonstrating how this is done kzitem.info/news/bejne/u4Bmn4yGqnSJZW0 :)
@PC_Simo
3 ай бұрын
2:27 I have a feeling that, if more than 1 point, on the arm, traces an ellipse of the same shape, these points would appear, periodically, along the arm; which would, on an infinitely long arm, imply that an infinite number of points would draw these same-shape ellipses.
@ketongu
5 жыл бұрын
man, that proof at the end was cool. an example of ostensibly difficult maths being broken down into fun, easy to understand fundamentals.
@MrCrashDavi
5 жыл бұрын
+
@artofpootan
3 жыл бұрын
0:32, Enjoy!....(pause for effect)....Bap! I took the first jab to the chin from The Nothing Grinder like a champ. Alright, let's continue.
@TheScienceBiome
5 жыл бұрын
I love how you present everything!
@robertt5992
5 жыл бұрын
Why didn't I get teachers who were capable of explaining mathematical concepts as simply as you?
@TheClimbingBronyOldColt
4 жыл бұрын
Schools: We will teach you to hate math! This video: Math, is actually fascinating!
@agod5608
3 жыл бұрын
The internet, the world's largest library club.
@charlesrockafellor4200
5 жыл бұрын
That was really pretty music at the end -- does it have a specific title or genre that I might learn more of it?
@MisterIncog
5 жыл бұрын
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).
@shadowhacker27
3 жыл бұрын
I'm sure Nadir discovered it while burning one the many libraries built by the many non-muslim philosophers back before their takeover, for which the Crusades was a neccesity for us to be able to snap out off. Thanks Christians!
@SteveFrenchWoodNStuff
5 жыл бұрын
Excellent explanation. Thanks!
@Mathologer
5 жыл бұрын
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 :)
@jafo4775
5 жыл бұрын
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.
@Ucceah
4 жыл бұрын
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
4 жыл бұрын
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
@mikefochtman7164
4 жыл бұрын
Great video. But near the end, 11:08 you mention that proving the point is on the diameter just requires proving 'these two arcs are the same length'. I understood how you proved the arcs are equal, but why does that prove the red dot is on the orange diameter? I don't understand how the arc lengths prove this?
@Jason-bd5iq
4 жыл бұрын
This is one of the most beautiful things I’ve ever seen in my life.
@shumeister1059
3 жыл бұрын
That's a usable design to create a rotary engine with 6 combusting chambers.
@LanceThumping
5 жыл бұрын
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
5 жыл бұрын
NerdyPi , true. Also the lenghts of the circles don‘t change over time.
@trogdorstrngbd
5 жыл бұрын
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.
@GarryDumblowski
3 жыл бұрын
It's hard for me to explain why, but since the line is an infinitely long RAY, i think there are three ellipses of that shape drawn on the nothing grinder. One on the very outside, and two smaller ones in the middle. I say this because the ellipse deforms from a circle, then to a line, then back to a circle again, and eventually back to a line as the tracing point travels towards the beginning of the ray. If it were a LINE instead, i would say there are four.
@satibel
5 жыл бұрын
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
4 жыл бұрын
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.
@el_teodoro
4 жыл бұрын
Do nothing? More like instant pizza cutter :D
@carlosmejia5728
5 жыл бұрын
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... 😎
@hertz42
4 жыл бұрын
Wow, randomly clicked this video, thought "man, this guy sounds German", googled him and found out that he did his PhD on my future university here in Germany. In German we would say: "Die Welt ist klein".
@unknownnepali772
5 жыл бұрын
THE BEAUTY OF "MATHEMATICS" ♥
@mettattem
5 жыл бұрын
Amazing video, as always, Mathologer! @5:00, your presentation of the invisible lines reminded me of a very interesting website that I stumbled upon in college, which presents the Whitney music box. The site is just whitneymusicbox.org... I'd love to see a future video about the Whitney music box! Keep up the good work!
@markmandel6738
4 жыл бұрын
Thanks! I'm saving that site in Pocket.
@gregsmith7828
5 жыл бұрын
it could be used to rive pistons or a well pump
@Mathologer
5 жыл бұрын
Here is a video of someone using this idea to cut an ellipse with a router kzitem.info/news/bejne/u4Bmn4yGqnSJZW0 :)
@KaitharVideo
3 жыл бұрын
That can't have existed this long without someone noticing ... it only needs a minor adjustment to get a really smooth rotary to linear motion linkage ... I wonder if there'd be too little force transfer
@mr.insectoid
4 жыл бұрын
Что я тут делаю?! Почему это у меня в рекомендациях?! Но это круто, соглашусь
@TheHenryFilms
5 жыл бұрын
The two-axis grinder looks exactly like a floating arm trebuchet! It's apparently much more efficient than the medieval one, I wonder if there's a mathematical reason why. Here's a video of it: kzitem.info/news/bejne/u6Z5vYewr6tmgmk
@Mathologer
5 жыл бұрын
That is very cool. Thanks for sharing :)
@DeFaulty101
5 жыл бұрын
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
5 жыл бұрын
Holding the distance between the pivots (P) constant, as the arm (A) -> ∞, P/A -> 0. Or, Lim A -> ∞, P/A = 0.
@AlanKlughammer
5 жыл бұрын
Or, since the eclipse is getting more and more "squished" it will trace a line.... Think about that for a while...
@inyobill
5 жыл бұрын
@@AlanKlughammer Look at the illustration at 1:31. It is clear that ellipses further from the center have lower eccentricty.
@AlanKlughammer
5 жыл бұрын
@@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
5 жыл бұрын
@@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.
@MPower-nf9if
3 жыл бұрын
I bet that final music was what Euler had always listened to after messing with a "problem!"
@alarageref2481
5 жыл бұрын
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
5 жыл бұрын
That's it, but there are some interesting exceptions (the extreme cases :)
@alarageref2481
5 жыл бұрын
Mathologer ahh there are two circles and two lines only. Mathematicians never miss an opportunity for pedantry :P
@inyobill
5 жыл бұрын
@@alarageref2481 One man's pedantry is another's precision.
@bentonpix
5 жыл бұрын
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
5 жыл бұрын
@@bentonpix Where did you get your Maths degree? This is an informal forum, and there is no ambiguity in the meaning.
@Zegger
5 жыл бұрын
Trying to defeat a goblin army on terraria while listening to this isn't funny
@UFBMusic
5 жыл бұрын
As a gay man in my 30s, I know everything I need to know about the Nothing Grindr...
@richardchambers3533
3 жыл бұрын
Right said Fred! I'm too sexy!
@lppunto
5 жыл бұрын
Like if you've been waiting for this since Thinkercon.
@Mathologer
5 жыл бұрын
Did you actually watch me talk about this stuff there? :)
@doctormarcelopizarro4012
3 жыл бұрын
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
@FireyDeath4
5 жыл бұрын
Fled when he begun to do the trigonometry.
@kallewirsch2263
5 жыл бұрын
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
5 жыл бұрын
/me pulls string on Talking Barbie Doll “Math is hard!” Moral: don’t get life lessons from a Talking Barbie Doll.
@SwedeEad
4 жыл бұрын
I've been meaning to make one of these for ages after watching a woodworker on KZitem 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.
@nikolaevkatesla3823
5 жыл бұрын
If you are daltonic you can not deactivate a bomb
@KnakuanaRka
5 жыл бұрын
NICOLAS TALLEDO I don’t get it.
@KnakuanaRka
5 жыл бұрын
Tony Morel And what exactly does that have to do with this video?
@JorgetePanete
5 жыл бұрын
@@KnakuanaRka nothing
@brendanward2991
5 жыл бұрын
Actually, you can. If movies have taught me anything, you will always end up with five seconds to choose which of two wires to cut ... and you will just have to guess.
@crackedmagnet
3 жыл бұрын
All through this video I was reminded of a geometric proof of sin2(x)+cos2(x)=1. At 8:10 I started to realise why.
@raymondstheawesome
5 жыл бұрын
too many vizualizations. we need some complicated formulas with little to no explanations of them!
@ogretowman
5 жыл бұрын
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
@Poordirtfarmer
5 жыл бұрын
Hello y'all from Suwannee County Florida 1st amendment auditors always watching an filming the Police 🚔
@Catdore
3 жыл бұрын
I see the innards of a radial aircraft engine.
@arisnikolopoulos9216
5 жыл бұрын
hey, mathologer, This is not Archimedes! This is Archidamus the 3rd!!! (Spartan king) Please don't help spread this misinformation. For some reason, many institutions have used this bust of Archidamus, even though he is obviously wearing an armour (why would a mathematician wear an armour?)
@lightspiritblix1423
4 жыл бұрын
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
4 жыл бұрын
Great :)
@stevengouws8684
3 жыл бұрын
Fantastic video's thank you
@CynicalOldDwarf
3 жыл бұрын
5:02 does anyone else see a weird optical illusion that makes the points of the circle look like they're shifting position instead of staying aligned as a circle?
@danielcohn6884
3 жыл бұрын
Yes, but my brain didn't acknowledge it until I read your comment
@Zyvo2
4 жыл бұрын
I wish you were my math teacher. This is far more interesting and applicative than the bs they taught me in school.
@the1gip
5 жыл бұрын
I don't know what's more lovely, your explanations or your mesmerising voice. Your delivery is utterly exquisite.
@williamgriffin4396
5 жыл бұрын
make it an engine 6 cylinders 3 pistons cars would burn less gas
@jet8062
5 жыл бұрын
I was thinking that
@visi2tirana
5 жыл бұрын
Thank you for these interesting and informative videos. 👌👌
@AlienRelics
5 жыл бұрын
I am going to use this information to make a device that illustrates how 3 phase electricity can result in a rotating magnetic field.
@brendanmorris4794
3 жыл бұрын
I love your videos. So much knowledge packed in an enjoyable, humorous package! Keep up the good work!
@mansardmanor3869
3 жыл бұрын
*A Nothing Grinder* Conquered the Wild West, think about the spinning railroad wheel's The gear is attached in the center of inner half circle
@justpaulo
5 жыл бұрын
10:55 Are you sure about the arc lengths thing? If the circles are perfectly rolling, w/o skidding, isn't that always true no matter the inner circle size? I think the proof kinda goes the other way around: b/c the arcs are the same, but the radii of the bigger circle is 2x the radius of the smaller one, you can say that the angle is 2x bigger for the smaller circle. And from that, and a bit more of geometry (similar triangles) you can then conclude that one end of the smaller circle arc lies always on the diameter of the bigger circle.
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