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 :)
My grandpa had one of these, labeled as the "Politician Machine", because it went round and round doing nothing.
Very much relevant still
Topical!
Yes very accurate
😂
based
This video really grinds my nothing
song title in there somewhere ...
how do you not have gears?
Sounds like a YIAY submission
One more plane and it would totally grind my gears.
@@ardinchesters128 hey! My man!
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.
*As a custom house builder* I too use it for in-situ arches
@@mansardmanor3869 lol
I wish my childhood teachers had shown half the love and passion for knowledge that you do. Thanks for your work!
Omg I know! I love how much he enjoys and appreciates what he talks about
0
First wish a good pay to teachers.
Me too, my childhood teacher just molested me
@@robertheller4583 weird flex but okay
The relationship between circles and triangles is one of the most fascinating. Enemies on the surface but secret lovers behind the curtains
Most underrated comment right here
^^^
Wtf.. lol
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. 🔴🔺🟥
"So let me inflict some really beautiful and surprising explanations on you..." He makes me feel like a mathochist
Badum bum.😄
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.
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.
I love the camaraderie among various KZhead 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.
10:20 Almost fell from my chair.
Have to do this more often then :)
Now get your BUTT back to the chair!
I know how you feel. I'm always excited by a nice big BUT.
Wake up at the back!
he used force
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.
are you sure that you don't get a similar elipse inside the circles, but rotated at 90°?
@@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.
@@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?
@@LucianoRobino Well, the smaller you go (like inside the green ellipse), the flatter the ellipse will get.
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!
What books?
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.
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.
@@VIM365 Bruh, who are you, chill down.
DJ KHALED people with huge egos strike a nerve
@@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.
David Diaz you know what? My bad dude. Sorry for being so harsh.
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).🤣
YES! Back in time (50 years) for me. :)
Yes I did, this video totally brought those memories to mind for me as well!
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
best x-mas gift I ever got! :))))))
Didn't know they were so old, pardon. But yeah I had one as a kid too. Lol
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!
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.
The Nothing Grinder? I've never heard it called that. I've always known it as the hillbilly entertainment center.
Another fun name to add to my collection :)
I always thought it meant Joe "The" Grinder, the reason for many a divorce.
Same
Heard it from vsauce
Ive always thought of it as a bullshit grinder
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.
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
7:36 "Yep, it's spirograph time" 😂😂
Donald Piniach what
This video is extremely well done! I love the animations and the 3D printer stuff.
:)
:) :) :))))))))))))))))))))))))))))) Guess which is me. Go on.
As usual, one of the best videos on KZhead. 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!
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.
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.
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.
man, that proof at the end was cool. an example of ostensibly difficult maths being broken down into fun, easy to understand fundamentals.
+
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!
I don't know what's more lovely, your explanations or your mesmerising voice. Your delivery is utterly exquisite.
Watching this makes me wish that I had a teacher like you when I was in school!
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
Exactly!
That's your reaction. Mine was, "thank god he isn't talking about conic sections". Your comment made me laugh though, thanks :)
It's just a simple way say it. Get of your high horse.
@@animationtime7265 and this was pretty obviously a joke, albeit a true one, chill.
A man of wisdom
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
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!
I love how you present everything!
Oh my, your t-shirts always crack me up soooo much 😂
Love the t-shirt. I want one :)
@@AaronRogge www.redbubble.com/people/theshirtyurt/works/24693541-math-puns-first-sine-of-madness?p=t-shirt&style=mens
Angle jokes? Don't be obtuse. Wait until at least he has acute one, right?
@@nacoran I went off on a tangent cos of reading his T shirt.
youre're*
Absolutely fascinating. As a cabinet maker I have used this principle many a time. I saw colleagues struggling with two nails and a piece of string- a touch-and-go method that’s extremely imprecise. In our Paris workshops we had a series of oval bullseye windows to make for a castle. The X Y (height and width) dimensions had to be precise. Okay, once you’ve determined the outer shape, how do you scribe the “parallel” inner one? This represents the width of the wooden frame. Solution: slide the scribing point inwards- towards the center- to the required width, say 90mm. Result: a perfect inner ellipse, equidistant from the outer one all around. Job done. I hope some concerned person will read this and understand the dilemma I had before I learned this principle. In woodworking shops we are not mathematically minded, so every bit of knowledge helps. Thank you for sharing.
THREE points on the arm will trace elipses with the same eccentricity (assuming non-zero). There is the point outside of the two slider-pivots as shown; there will also be two points BETWEEN the pivots, one that traces that eccentricity with a horizontal major axis, and one that traces it with a vertical major axis. This assumes the arm extends only in one direction, like a ray. If it extends as a line in both directions, there is a FOURTH point that traces an ellipse of any given eccentricity 0 < _e_ < 1. The point on the other side of the pivots would trace your example with a vertical major axis, rather than horizontal.
Man, I really love your videos. Thanks for your work, honestly.
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.
Yes, its a great effect :)
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.
So you can try it as many times as you like: 4:46
I was thinking different color dots in flash would be a trip. Transitions from one color to another as it travels across the line.
My father used to make these in his woodshop, he called his "smoke grinders".
I love your videos. So much knowledge packed in an enjoyable, humorous package! Keep up the good work!
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!
Great :)
Drinking game, take a shot each time he says "neat huh?"
This is one of the most beautiful things I’ve ever seen in my life.
I've been meaning to make one of these for ages after watching a woodworker on KZhead 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.
One minor point I did not see covered in this excellent nothing-grinder video is that the spacing of the points on the small circle need not be regular, and can in fact be random or even chaotic. Such irregular placements result in grinders where the angles between adjacent tracks can vary vastly in scale. To construct a virtual (or real) example of an irregular grinder, place n points randomly around a circle. Connect them to form an irregular convex polygon, and use that polygon to build a rigid rotor with sliding pins at each vertex. Add one more point to the rotor circle to represent the center of the larger circle, and extend lines from this new point to each of the n vertices of the rotor. These lines define the tracks for the sliding pins of the polygon rotor. If the center of the big circle happens to fall exactly on a rotor vertex, the track for that vertex is tangential to the circle. No matter how oddly shaped the polygon rotor is, and no matter how many vertices and tracks it has, the resulting system can in principle exhibit the same smooth circular flow as a classic nothing grinder with only two vertices (a bar) and two tracks. Note that for any given irregular polygon rotor there would seem to be an infinite number of possible track arrangements, depending on where the final point is placed on the rotor circle. This is an illusion, however, since the track lines end up having the same relative angles regardless of where the final point is placed.
7:30 Suddenly I saw a toy I played back when I was in Grade School!
Wow, I like this guy's presentation so much. The KZhead trend is towards more yelling, hyperbole, "excitement"
Hyperbole, hyperbola
He sounds like he is bored
Burkhardt, your love and enthusiasm for math and logic shine through vividly. THANK YOU!!!
5:00 this reminded me of those colorful beads we would put on our bikes wheel. They made that clacking sounds when you were driving as they were sliding up and down the wires and colliding with each other and wheel frame.
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... 😎
When I saw this I thought of the Spirograph toy which is essentially the same.
At 7:08 this finally reminded me of a toy i had when i was a child. it was in 2 pieces. large one had teeth on inside and small one had teeth on outside. It allows you to draw patterns that look like flowers.
I’m now 70 years old and have very seldom had to use algebra, trig and geometry since I left secondary school! I worked in electrical technology, electronics and medical imaging systems ( service technician ) . I don’t think I will extend my life because of this device. 🤔🤔🤗🤗🤗
Excellent explanation. Thanks!
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 :)
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".
indeed
Supposing prononciation was unchanged over 800 years and shared through ethnicities
@@2adamast surprisingly few changes. "Moon" and "Sun" consonants didn't change in High Arabian, although they aren't used now colloquially.
this contradicts itself
because it disappears instead of doubling
That is awesome that you made and provide those print files. Hats off Sir.
When the dots are spinning inside the larger circle, it just looks like a wheel going round and round, but once you draw the straight lines that make up the path of each of those dots, it starts to look SO different, eventho it is the same movement!
THE BEAUTY OF "MATHEMATICS" ♥
"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
I gave one of those to my dad when I was a kid, at least 60 years ago. My dad loved it. He was an inventor and a designer a mechanical items. I think I know why my dad was so thrilled to get one. He knew exactly what it was and how to use it and he was fascinated with it. It is the type a thing my dad would enjoy.
I wish you were my math teacher. This is far more interesting and applicative than the bs they taught me in school.
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.
Very good :)
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.
Damn, I thought this was about a weed grinder, but left with knowledge. Amazing video!
Learning math is so cool, lol
It won't grind weed but watching it will save on weed
@@crhu319 actually I wanted to smoke more watching this due to it being so cool lol
KZhead recommend this to me, and boy am I glad they did. Thanks for the video. I look forward too more.
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.
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.
I think it's a possibility to turn this "Nothing grinder" into a working engine...
it's the rotary engine's less successful brother
10 second into this i was thinking the same thing. i feel a compression engine would benefit the most
JoshTheKid You are thinking of a radial airplane engine.
The gear for a hand crank power generator
@@lil0of I think you mean Wankel.
What a completely fantastic video! Utterly amazing! Subscribed straight away.
I am waiting the next excitement &educational video of @Mathologer. Always with his nice sense of humor.
So is the rotary engine a complex "do-nothing" machine? Can you verify or am I just over thinking the Mazda power plant?
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
I was thinking the same. I wonder if a radial engine is also a nothing grinder...a simple one.
Nah, to me it looks more like a radial aircraft engine.
you guys got it all wrong. you want a 1024 cylinder engine
Jim Beam the wankel is different becaue of internal combustion.
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 KZheadr rrrrreally impresses me. Just for fun, I go outside & humbly bow to them in their general direction. ?Where about do you live?
Glad you like the video so much. Melbourne :) What sort of things did you work on as a military physicist?
@@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" kzhead.info/sun/mpWRYaqHkZ-jiXk/bejne.html ). 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 KZhead 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.
@@tombouie :)
@Matrix29bear Hmmm, I'm retired/clueless on common core stuff but you might be interested in these: The College Meltdown @CrushTheStreet kzhead.info/sun/oceqqtJ-pHOkoKM/bejne.html Default: the Student Loan Documentary (Broadcast Version) kzhead.info/sun/qtqKgp1remikZX0/bejne.html How college loans exploit students for profit | Sajay Samuel kzhead.info/sun/jLyQe9mDZIOpqGw/bejne.html For these college students, the most difficult test may be basic survival kzhead.info/sun/aaajpq6RgZesiaM/bejne.html Elon Musk, Jay Z, Warren Buffett, and other's criticism on college kzhead.info/sun/q81xdLeenqWpYHA/bejne.html The Reset Button: The Great Fantasy of Academia | Brian Harrington | TEDxUTSC kzhead.info/sun/ddp7lKxteH2igZs/bejne.html The Truth About PhD Unemployment Data kzhead.info/sun/edimkZaGm2Wwnok/bejne.html The Biggest Scam in America kzhead.info/sun/p7ygc6ttZ4uliqs/bejne.html Ferengi Rules of Acquisition kzhead.info/sun/g9p_iaajnKWneo0/bejne.html 6 Problems with our School System kzhead.info/sun/os-pl5GkjYmClX0/bejne.html Why I Hate School kzhead.info/sun/lbRtib6mqGalgXk/bejne.html How School Makes Kids Less Intelligent | Eddy Zhong | TEDxYouth@BeaconStreet kzhead.info/sun/Zb2tZtaZoV-JZIU/bejne.html&vl=en How School Prepared You To Fail kzhead.info/sun/l9yJht6ci2Oiemg/bejne.html Do schools kill creativity? | Sir Ken Robinson kzhead.info/sun/nKtyc6ltbKmYp5E/bejne.html Humans Need Not Apply kzhead.info/sun/arSqXbdtbGmOhI0/bejne.html The Rise of the Machines - Why Automation is Different this Time kzhead.info/sun/ireEmZyAnZWueKM/bejne.html
@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.
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
Mathologer is my favorite channel ever. And yes, I owned a Spirograph as a Child. A great toy!!
Schools: We will teach you to hate math! This video: Math, is actually fascinating!
The internet, the world's largest library club.
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).
Ngl I'd want this guy to teach my math class, he's so straight forward and explains things so well.
You would really get a kick out of checking out an old B-29 bombers engine. It had 36 cylinders. 4 banks, corkscrewed with 9 cylinders per bank, all driven by one true connecting rod. This was made before calculators and computers. Fascinating. Love your shirt by the way....
My grandpa made one of these for me! He called it a BS grinder 😂
a blue shape grinder?
Mine too! Forgot all about it. He made it in the 70's.
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, )
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
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.
Wonderful demonstration.
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.
NerdyPi , true. Also the lenghts of the circles don‘t change over time.
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.
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.
That's it, but there are some interesting exceptions (the extreme cases :)
Mathologer ahh there are two circles and two lines only. Mathematicians never miss an opportunity for pedantry :P
@@alarageref2481 One man's pedantry is another's precision.
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".
@@bentonpix Where did you get your Maths degree? This is an informal forum, and there is no ambiguity in the meaning.
Thanks, great video. This is very much like the action of a Geneva Mechanism. I operate multiple spindle automatic screw machines. Several spindles are arranged in a large cylindrical carrier. Between each tooling operation, the carrier is indexed one eighth of one rotation. This is accomplished by the Geneva Mechanism, which divides carrier rotation accordingly.
This is one of your best videos yet, to be honest. I really liked the visuals in this one
"Typical mathematical denial of reality." :)
As the arm's length approaches infinity (relative to the distance between the pegs), I imagine the oval produced would approach perfect circle-shape.
Holding the distance between the pivots (P) constant, as the arm (A) -> ∞, P/A -> 0. Or, Lim A -> ∞, P/A = 0.
Or, since the eclipse is getting more and more "squished" it will trace a line.... Think about that for a while...
@@AlanKlughammer Look at the illustration at 1:31. It is clear that ellipses further from the center have lower eccentricty.
@@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.
@@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.
I used a nothing grinder to cut oval shapes on a prototype for a teardrop camper. When you put a router on the end of the stick it does really grind more than nothing.
Wow in just few min from someone i never met helped me to pull together answers to years worth of questions i thought i would never get an answer too or even understand the outcome put together that way thanx soo much....
it could be used to rive pistons or a well pump
Here is a video of someone using this idea to cut an ellipse with a router kzhead.info/sun/ja5pabyIqHSOZXA/bejne.html :)
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.
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.
Beautifully illustrated....... With passion
11.23 it goes an eighth round large and quarter around small circle, love the simplicity man...
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.
Thanks for pointing this out. Here is a video of someone demonstrating how this is done kzhead.info/sun/ja5pabyIqHSOZXA/bejne.html :)
*Évariste Galois approves*
Really beautiful graphic animations! Mesmerizing, and inspiring.
My grandfather was a highly skilled woodworker, and he made one of these as a toy for us kids. Fifty years later, I see some of the related math!
Fled when he begun to do the trigonometry.
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 :-)
/me pulls string on Talking Barbie Doll “Math is hard!” Moral: don’t get life lessons from a Talking Barbie Doll.
You may call them nothing grinders, but they actually show how combustion engines work. I wouldn't call that nothing.
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.
@@RR67890 I could say you're nitpicking, but maybe a better term would be piston engine.
Love the shirt and your humorous approach.
Hi ,They are useful, As a Contract designer I used this type of device on an inclined ramp with a swinging arm attatched to slide components off into boxes. It was successful, solving a problem they'd had for years of parts accumulating in a heap. Basically it converts rotary motion into linear motion.
Great, would be nice to see a video of this sort of device in action :)