@@ankitaaarya A diameter is a line from one point to another of a shape (not just circles and spheres) which passes through the center. So, it does apply in this case.
@@royalninja2823 but it doesn't because the distance from the center of the object to the surface is not constant in these shapes. ONLY a sphere has that property. With these shapes, what is constant is the distance between the "Top" and the "bottom" but this line does not always go through the center of the shape. Hence why the term constant width is used, instead of the incorrect constant diameter, because diameter is defined in terms of a center, while width is not.
I wanna know at what age this man found his passion for all these fascinating objects and hope that I will be as passionate about something by that time
I discovered his website circa 2005. The videos were on his website and not youtube. The youtube channel started in 2008. The website was started in 1996 (as per the info available). He has shown things he ha had for decades so I guess the passion must have started at an early age.
The conundrum for me is that the objects are of constant diameter (as you said), when "constant" diameter would normally refer to a sphere, which these are not. The lowering of the uppermost point, while rising of the lowermost point (while in constant contact with their respective positions), makes this an elegant application. If the "weight" could also be equally distributed (non-moving center of gravity), the applications for this would be limitless. Very ingenious!
The mass is equally distributed (assuming uniform density). And thus the center of mass is also stable. I think you meant that this object doesn't have a constant distance from the center of mass to any surface point (radius?).
frankensteinmoneymac They wouldn't make very good wheels since the distance from center to edge, or "radius", is not constant, what is constant is the width or "diameter"
+Buffoonery Hokey smokes! Who woulda thunk it! Me, the second smartest person in the world, learnt sumthin new. I looked at the picture, I think, 'Why neither of those is a radius, neither is half a diameter. (R=D/2) What kind of buffoon does Buffoonery take me for? Lessee what Wiki sez.'.... Low and be whole!! "... the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure." !!! Then there's all kinds of big letters and lil numbers and check marks and low numbers up high and high numbers down low and stuff in parenthesis that they don't want spoken of out loud, just thought about. Also says " The plural of radius can be ... the conventional English plural radiuses. Not for us, radii is fine for i and mine.. Radiyouses take that side of the diameter, radiuses will take this'n. " Low and be whole!! " said the faith healer to the butchered cow. I just made that up. A moment of hysterical history of which you are a witness.
if you roll some putty with your hand against a table at a constant distance, you can achieve a ball or sometimes this shape here. found it out a while back but never knew the technical term. thanks Tim!
I was wondering how shapes like these are created, but then I think I figured it out from thinking about spheres. I don't know the correct geometric terminology to explain, so I'll use Earth as an example. Imagine Earth as a perfect sphere, then take the equator (just the line) and shift it either up or down along the Earth's axis (if the axis went perfectly straight through the earth and didn't wobble). Imagine that the crust of the earth (the surface of the sphere) adjusted and conformed accordingly by curving and increasing/decreasing surface area to match the new "equator" position. So...yeah. If anyone can understand, I like feedback. Something I came up with in like 30 seconds.
Basically its intersections of Spheres where every point on an edge or corner is the center of one of the spheres. in that case the "topmost" point is the center of the bottom sphere section and each of the points of the edge is the center of exactly one line of the top surface that makes the diameter constant even though its not a sphere... for example in a 2 dimensional case, draw a triangle and use every corner as a center point and the side of the triangle as a radius (draw the curve from one corner to the other), you'll end up with a non circle, that still has the same diameter everywhere. I hope that was kinda understandable...
maybe you could use it for smooth camera movements
11 ปีที่แล้ว
British 20p and 50p coins, among other coins, have the same quality. Even though they are not shaped like a circle, they run in a coin slot like round coins. Also there is an engine called Wankel engine, which has a piston shaped like a triangle of constant width. Then there is a drill bit that uses this to drill a hole that is shaped like a square.
Just because you can't think of a use for it now, does NOT mean it's useless. The man who discovered radio waves had no idea what they could be used for. It was't until some time later that someone discovered a use for them.
Everything in their shop is so overpriced. These are probably pumped out 100/hr on a CNC lathe with 1 bloke sitting beside it being payed $20/hr to hit go and change the tool tip when it wears out. Even after the rest of the overheads they're still on a huge profit. Change that 20 dollar an hour worker to a 2 dollar an hour worker in China with half the overheads still and the profits are even greater.
This reminds me of a problem when making sure early subs wher round. They realized that just checking oppoisite sides was not enough, hence you get what you see here.
Yes there is, you can fit a board whose length and width that are bigger than the length and width of the square hole, through that hole, you cant fit it through a circle hole.
If you ARE gonna split hairs, sure, you might have a guest over who is inspired with a brilliant idea upon discovering these objects. But as far as curiosity, fascination and inspiration goes, then just about anything would be useful. In a more immediate and practical sense, however... I never meant to put in doubt their potential usefulness and applications. Only that they're not serving much purpose as book bases, not in an obvious manner, that is.
The surface is the same distance when measured from the bottom and not when measured from the center. A sphere is the same when measured from both. That is what gets the mind here.
If i fill a room full of these things, and slide a book across the room, will the book slide over these things, or will hit some and fall on the floor?
Obviously they aren't to be used as ball bearings, but consider a device which should only easily move a certain distance. A great many things can be done with a little imagination.
I know you don't mean to be rude. I believe that some car company (mazda?) used one of these nonspherical shapes in its engine. I think they used a triangular one.
there is an issue mathematically as well unless its a circle there is no such thing. you would learn this in geometry when learning about measuring triangle lengths and the same rules apply
so if you made this into a wheel with the axel changing dynamically with the rotation of the wheel, could you make it smooth? also, even better, could you make the shape out of multiple different materials so that it is balanced and rolls like a sphere ?? the current design leaves it heavier on one end. what if you preserved the shape but instead made some of that bottom portion out of a lighter material?? you could roll it right?
It would still oscillate way more than a sphere, even if the weight was distributed. Because the radius isnt consistent. Yeah, in theory a moving axle could compensate but that is just a ton of work for something that works (at best) the same as a circle.
well, yes those drills use the same shape as this thing if you would saw it in half, but these solids as they are now seem pretty useless as loose paperweights...
I feel I got scapegoated in order for interesting things to be pointed out, heh. Since most of the replies did indeed have interesting info to learn. This event in itself is curious, even ironic... I've a top comment on the ice heart maker video for a year now; here it went the opposite way. Definitely the bottom comment, hahah! Well, most replies were polite. If they served to enlighten other folks (whether they incidentally voted me down or not, heh), then so be it, it was worth it.
Never knew this is actually possible (never thought about it), that there are non-spherical solids of constant diameter. Amazing!
I don't think so, definition of diameter requires you to have a sphere
@@ankitaaarya A diameter is a line from one point to another of a shape (not just circles and spheres) which passes through the center. So, it does apply in this case.
Irrazzo ask yourself interesting useless out of this world questions and this is the type of result you get
@@royalninja2823 but it doesn't because the distance from the center of the object to the surface is not constant in these shapes. ONLY a sphere has that property. With these shapes, what is constant is the distance between the "Top" and the "bottom" but this line does not always go through the center of the shape. Hence why the term constant width is used, instead of the incorrect constant diameter, because diameter is defined in terms of a center, while width is not.
@@MassDefibrillator Nice rebuttal!
I wanna know at what age this man found his passion for all these fascinating objects and hope that I will be as passionate about something by that time
Amen
I discovered his website circa 2005. The videos were on his website and not youtube. The youtube channel started in 2008. The website was started in 1996 (as per the info available). He has shown things he ha had for decades so I guess the passion must have started at an early age.
What is your pfp?
@@christinaandwena8917 Nostalgia and pain.
he’s an engineer, it’s part of him to be curious so he’s just a very curious person who found toys and experiments fascinating
Solids of constant width is a good sign of healthy bowels.
Heh.
rabbits have been perfecting it for years
Orange Harrison: wonderful comment : )
Solids of constant width would be cylinders.. which.. would probably be very painful
Spheres not cylinders, I hope you are not effing with me.
Solids of constant width would be a good name for a band.
+sisyphis I'm fucking done XD
ayyyy
The moment you realise people are tori. The mouth and the anus are the same hole.
Chris Daley mindblowing
Someone (not me) give this man John a million dollars
a perfectly "round" object that automatically sits the same way when left alone (compared to rolling around randomly)? I'm sure there are uses :)
A sphere with an off-center weight inside it would work just as well (but I guess it wouldn't be as cool).
Xezlec lol
Sounds like me
@@DavidNorthMusic Have you found a use yet?
@@poika22 Give me a fishing rod and I make for an interseting garden feature.
Book name: How round is your circle. A perfect name for this.
Lmao nice hidden joke
Take a look at what's on the cover
Everyone: *mildly interested*
Engineers: *jizzing their pants*
Over this??
@@thememaster7 yes
@@birb2197 Why?
@@thememaster7 Because they are Engineers
@@chyren_ran No shit. I'm asking why it's enough to make engineers be this way.
Gotta love how, if you don't see the thumbnail, the book's cover is gonna clue you in anyway.
Wow, I didn’t even notice what the cover said
I can answer it’s question. Not round at all, it doesn’t matter if I’m using my lucky pencil or not my circles are awful
Plug
I never expected there to be a book named "how round is your circle?"
As I've aged & become more sedentary, I too am a constant width.......😮
Oh that's how those plugs work...
Think you hit it right in the butt
oh god
we’ve been using them the wrong way!
The conundrum for me is that the objects are of constant diameter (as you said), when "constant" diameter would normally refer to a sphere, which these are not. The lowering of the uppermost point, while rising of the lowermost point (while in constant contact with their respective positions), makes this an elegant application. If the "weight" could also be equally distributed (non-moving center of gravity), the applications for this would be limitless. Very ingenious!
The mass is equally distributed (assuming uniform density). And thus the center of mass is also stable. I think you meant that this object doesn't have a constant distance from the center of mass to any surface point (radius?).
Constant diameter doesnt refer to a sphere anymore than quadrilateral refers to a square. Constant RADIUS refers to a sphere
Ik this is 9 years old, but wouldn't the application just be the exact same as spheres?
It is not round in shape but yet it is as round as a ball. Mind blowing stuff I must say dear chaps!
I imagine this is based on the Reuleaux triangle, except in 3D form. One could call it the Reuleaux cones. :3
Yup, it's just a rotation of the reuleaux triangle. I think a more elegant object of constant width is the meissner tetrahedron.
Reuleaux Tony Brown Town
My mind is blown! Totally fascinating!
There is definitely a really good use for this idea.
I just can't quite think what it is yet?
Upvoted! I think rotary engines are also a cool example of this being used! (although they are the 2D equivalent)
So basically some mathematician literally reinvented the wheel using a shape other than round. Science....U so crazy.
Well, they ARE round, depending on your definition of round, that is...
frankensteinmoneymac They wouldn't make very good wheels since the distance from center to edge, or "radius", is not constant, what is constant is the width or "diameter"
+MiauFrito If the diameter is constant, the radius has to be constant.
+John Statser
I'll show you a picture of how it works :)
prntscr.com/adcbhp
R1 + R2 = D1
2.25 + 1.75 = 4
2 + 2 = 4
1.9 + 2.1 = 4
...
etc.
+Buffoonery Hokey smokes! Who woulda thunk it! Me, the second smartest person in the world, learnt sumthin new. I looked at the picture, I think, 'Why neither of those is a radius, neither is half a diameter. (R=D/2) What kind of buffoon does Buffoonery take me for? Lessee what Wiki sez.'.... Low and be whole!! "... the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure." !!! Then there's all kinds of big letters and lil numbers and check marks and low numbers up high and high numbers down low and stuff in parenthesis that they don't want spoken of out loud, just thought about.
Also says " The plural of radius can be ... the conventional English plural radiuses. Not for us, radii is fine for i and mine.. Radiyouses take that side of the diameter, radiuses will take this'n.
" Low and be whole!! " said the faith healer to the butchered cow. I just made that up. A moment of hysterical history of which you are a witness.
the how round is your circle book is a nice touch
after a year and a half of being subbed to this channel, this shit's still got me fucked up.
+CycloneMetal
prntscr.com/adcbhp
R1 + R2 = D1
Hey I found them in my step sisters room too! Those are cool as hell to play with.
LMAO
love how the book is also related to the topic
how this guys knows so much about everything
Literally saw a yt short with the exact same concept, except instead of book it was glass. Tim was 10 years ahead of his time.
This is such a charming series
if you roll some putty with your hand against a table at a constant distance, you can achieve a ball or sometimes this shape here. found it out a while back but never knew the technical term. thanks Tim!
I watch one video.. because it got recommended.. and BOOM.. I'll see these in my inbox for the next few months
I was wondering how shapes like these are created, but then I think I figured it out from thinking about spheres. I don't know the correct geometric terminology to explain, so I'll use Earth as an example. Imagine Earth as a perfect sphere, then take the equator (just the line) and shift it either up or down along the Earth's axis (if the axis went perfectly straight through the earth and didn't wobble). Imagine that the crust of the earth (the surface of the sphere) adjusted and conformed accordingly by curving and increasing/decreasing surface area to match the new "equator" position.
So...yeah. If anyone can understand, I like feedback. Something I came up with in like 30 seconds.
How much hash did you smoke before not figuring this out?
That says a lot more about you then it does about me.
I need to smoke a lot of hash to understand this.
Basically its intersections of Spheres where every point on an edge or corner is the center of one of the spheres. in that case the "topmost" point is the center of the bottom sphere section and each of the points of the edge is the center of exactly one line of the top surface that makes the diameter constant even though its not a sphere... for example in a 2 dimensional case, draw a triangle and use every corner as a center point and the side of the triangle as a radius (draw the curve from one corner to the other), you'll end up with a non circle, that still has the same diameter everywhere. I hope that was kinda understandable...
TheSwissGuy1 almost forgot, an equilateral triangle of course ;)
Wouldn't it be so much simpler simply to make a ball?
+abstractbybrian Where's the fun in that? Who knows where applications of this will lead? Even simpler is to make nothing at all.
+abstractbybrian A ball will roll off on you. These will settle.
abstractsbybrian like Germans...
OVER ENGINEERED!!!
Here I am trying to favorite the cool videos... The fun part is that every single one I tried to favorite was already in the list.
haha i like the book you chose for this video, "how round is your circle"
Most excellent solids of constant width indeed
Stand name: [Objects of constant diameter]
English localization: [Solids of constant width]
Why is this actually like really cool lol. Clicked on this vid thinking "eh....." and now I'm just o.o
*Everybody gangsta untill you fall backwards on top of these things*
maybe you could use it for smooth camera movements
British 20p and 50p coins, among other coins, have the same quality. Even though they are not shaped like a circle, they run in a coin slot like round coins. Also there is an engine called Wankel engine, which has a piston shaped like a triangle of constant width. Then there is a drill bit that uses this to drill a hole that is shaped like a square.
now you are just making stuff up mate!
Title of the book. Extraordinary.
love the choice of book…genius!
I love your enthusiasm sir. Henders !!!!
It's just the little things, that seem so amazing.
But, could you make wheels like this? Can you run an axle through the center point and remain at a constant height from the ground while moving?
Just because you can't think of a use for it now, does NOT mean it's useless.
The man who discovered radio waves had no idea what they could be used for. It was't until some time later that someone discovered a use for them.
I am pretty sure these shapes use the exact same amount of material that a sphere with a corresponding diameter uses.
Cool! The solids have constant diameter, but not constant radius.
They would have to have a constant radius if the diameter is constant or maths would broken
Oh dear. There goes my brain again. Excuse me while I mop up the ceiling.
Blows my mind, how does the math work?!
50 bucks for a set of these...I bet you 50 bucks I can move a 2-ton slab bare hands with these and win. Pays for itself.
Yeah, or get three ball bearings, cheaper.
If you where entering a 2 ton slab moving competition with the main rule no spheres allowed, then you might win that I suppose.
Everything in their shop is so overpriced. These are probably pumped out 100/hr on a CNC lathe with 1 bloke sitting beside it being payed $20/hr to hit go and change the tool tip when it wears out. Even after the rest of the overheads they're still on a huge profit.
Change that 20 dollar an hour worker to a 2 dollar an hour worker in China with half the overheads still and the profits are even greater.
MPAH1981 i guess you'd rather pay mexicans for that labor?
MPAH1981 These things are precision machined.
This reminds me of a problem when making sure early subs wher round. They realized that just checking oppoisite sides was not enough, hence you get what you see here.
would bowling balls work if they were shaped like that?
Smoothly.
Yes there is, you can fit a board whose length and width that are bigger than the length and width of the square hole, through that hole, you cant fit it through a circle hole.
His voice is really relaxing
Wow. That’s incredible
its almost 3am and im clicking on video with titles I dont understand
So what.. ? The square block has to go into the square hole and the triangle into the triangular hole. Something more obvious to tell?
Did anyone realize how perfect the book fits the video?
so are spheres
these have an edge (or less than infinite edges) meaning this is not a sphere
who else is going down this rabbit hole of just watching these vids for no reason?
If you ARE gonna split hairs, sure, you might have a guest over who is inspired with a brilliant idea upon discovering these objects. But as far as curiosity, fascination and inspiration goes, then just about anything would be useful. In a more immediate and practical sense, however...
I never meant to put in doubt their potential usefulness and applications. Only that they're not serving much purpose as book bases, not in an obvious manner, that is.
everything is quite extraordinary on your channel
Wonderful invention, indeed!
How round is your circle?
The surface is the same distance when measured from the bottom and not when measured from the center. A sphere is the same when measured from both. That is what gets the mind here.
But i can see that they dont have constant diameters!
TF?
I'm ten years late but I love these things
I’m really trying but I still dont get it
So can we make a tyre shaped like this?
Really rather extraordinary.
If i fill a room full of these things, and slide a book across the room, will the book slide over these things, or will hit some and fall on the floor?
Obviously they aren't to be used as ball bearings, but consider a device which should only easily move a certain distance.
A great many things can be done with a little imagination.
0:34 that looks so cool.
embarrassingly i am enchanted
I know you don't mean to be rude. I believe that some car company (mazda?) used one of these nonspherical shapes in its engine. I think they used a triangular one.
It also includes minimal surface area
(To the tune of ‘man of constant sorrow’)
A man of constant sorrow had solids of constant width.
That's all good but exactly how round is your circle?
This makes me happy
Ok so nobody searched for this video... let's agree on that
there is an issue mathematically as well unless its a circle there is no such thing. you would learn this in geometry when learning about measuring triangle lengths and the same rules apply
so if you made this into a wheel with the axel changing dynamically with the rotation of the wheel, could you make it smooth? also, even better, could you make the shape out of multiple different materials so that it is balanced and rolls like a sphere ?? the current design leaves it heavier on one end. what if you preserved the shape but instead made some of that bottom portion out of a lighter material?? you could roll it right?
It would still oscillate way more than a sphere, even if the weight was distributed. Because the radius isnt consistent. Yeah, in theory a moving axle could compensate but that is just a ton of work for something that works (at best) the same as a circle.
Would a sphere not do the same?
Solids of constant width != Width of constant solids != Constant width of solids != Constant solids of width ...
why not just spherical? is it because there will be no width,then or rather that this geometry allows for certain engineering feat to be accomplished?
Extraordinary.
well, yes those drills use the same shape as this thing if you would saw it in half, but these solids as they are now seem pretty useless as loose paperweights...
Anyone wanna note the name of that book
If I remember correctly, this same sort of idea is used in rotary engines.
They look like acorns. Are there any acorns of constant width?
I feel I got scapegoated in order for interesting things to be pointed out, heh. Since most of the replies did indeed have interesting info to learn. This event in itself is curious, even ironic... I've a top comment on the ice heart maker video for a year now; here it went the opposite way. Definitely the bottom comment, hahah!
Well, most replies were polite. If they served to enlighten other folks (whether they incidentally voted me down or not, heh), then so be it, it was worth it.
This sounds like spheres with extra steps but cool
also fellas, how round is your circle?
There are forklifts that use this technology in order to turn smoothly in narrow spaces.
The book reads how round is your circle
Not only that, the book is about these small devices themselves.
don't worry [whatever you believe in or not believe in] will patch it on the version 1.0.25.1
So, no different from a circle?
ah yes, numberphile
How to move heavy stones ?
Me halfway through the video: So? The book is resting on some objects
Me 2 seconds before the video ends: Wait a minute!