Of course, being solids of constant width doesn't mean that your next car will be exhibiting them. When wheels are fitted to cars, it is the distance from the axle to the ground that is important to prevent bumps. These shapes have constant 'diameter' (a bit of an abuse of the word diameter there, but oh well), but for wheels you want shapes of constant 'radius' (of which there is only the circle).
Quite right. That's why I say "rudimentary" wheels (trying to skirt the issue without going into detail!). Good spot though. Glad someone brought it up in the comments.
+SpySappingMyKeyboard But there are vehicles, such as motorbikes that use wheels without axles, called hubless wheels. Wouldn't wheels with constant width which aren't circles work in these cases?
KiloOscarZulu I don't know much about hubless vehicles, but the designs I've seen all have a fixed joining point. The problem is how to connect an irregular 'wheel' to the vehicle, since the special thing about these shapes is that their height never changes. Although, you could perhaps make a specific design that sits on top of a 'wheel' and uses the irregularities to spin it. However, I think reinventing the wheel is as fruitless as it sounds :D
Wheels do not make contact at a single point, they flatten out at the contact area and deform a very high amount. Making a car with the triangular shapes of constant width would not only be hard to produce, but they would be prone to stress tears and TERRIBLE wear patters. Basically: although the width of them stays the same, the surface area of a shape of constant width is not the same throughout. A circular wheel would have a near constant surface area in contact with the ground. Edit: Take a look at 0:15 seconds in ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-E_u0YR10Vo0.html Although regular car tires are not this extreme, the same stresses occur which would be hell on the irregular lines of stress through a triangular shape of constant width.
Shapes of constant width but not constant radius. If you try to turn them in to wheels by putting them on an axle you'll get a bumpy ride. They'll work fine as rollers as the book demonstration shows.
Yep, I was just about to comment the same. Objects of constant width aren't going to be good wheels without some extra, likely overly complicated engineering vs just using something more circular.
@@karmanyaahm It's the best way to tell if someone is Canadian vs Amarican-how they pronounce their "-out"s ...because we sound the same every other way
@@ChadDidNothingWrong No, most Canadians say about the same way as Americans. Only people from newfoundland really say aboot..... Its a misconception. And really somone from newfoundland has a pretty distinct accent which is why they say it like that.
neat but they would Not be good wheels with an axle. because the axle would have to be in the center and measuring out from the center it would not be a constant with.
+Zutaca Well, if the shape keeps a constant diameter (see Releaux triangles), it can still roll - although you can't place an axle through it as where the axle should be would keep changing
technically yes they can work as wheels, but they would wear at the vertices because the wheel spends more time grinding on the ground there (eg - the a large portion of the curve in the rounded equilateral triangle is directly facing a small vertex on the other side - so when the curve points up, the vertex grinds the ground, while when the vertex points up the time on the ground is shared by the whole curved side). Also, if filling them with air (or any other substance) you'd end up with weak points that aren't there in a circle. You'd also need some sort of gear assembly on the inside of the wheel to allow the axle to stay in one position... But then all of the stress from the axle is concentrated on the gear teeth, so you've got another unnecessary weak point.... I guess the answer is no.
There are a few, but look up AvE's channel and a video of the Trailer Park Boys for two examples from different sides of the continent. If you want more of a Prairie sound Corner Gas and Letterkenny Problems (Letterkenny's Ontario though) are good ones to check out.
Not really. Lived here 21 years, and nobody has a "Canadian" accent, or even the traditional "Minnesotan" accent used in the movie "Fargo", which has scenes in my hometown, Brainerd, that sound just completely foreign to me.
I love Matt bursting with pride while Steve was saying that Australia was one of the first countries to make polymer notes and that most polymer notes are made in Australia. I have to say, I was too. Oh and that perfectly cut ending was **chef's kiss**
+Steve Mould - Science Videos They are only "not" a bumpy ride because you put both sides of the coin towards a wall. A wheel only touches 1 side at a time and with an axel in the middle you would get a very bumpy ride. The axel is possitioned in the middle not at the oppisite side of the edge compared to the ground.
You can't actually use a shape of constant width as a wheel for the simple reason that, while the width remains constant, the distance between the center of the shape and the point it contacts a surface doesn't, so you could never fit them on an axle
When I was ten years old I managed to stack 8 of those Australian 50 cent coins on top of each other. I used to scavenge through loose change looking for coins in the best condition; with the truest edges. 6 was easy. 7 took a lot more effort, and I only achieved 8 once. Years later it occurred to me it might have been a lot easier to place them all on a horizontal ruler, then slowly incline the ruler to the vertical.
The coin can't be used as a wheel because wheels require constant radius, not constant diameter. If all you have is constant diameter, there's nowhere you can put an axle. This is particularly clear with the Reuleaux triangle you show at 1:25 -- the centre is jumping around all over the place. You could glue a bunch of the coins together into a cylinder and use it as a roller but that's not a wheel.
Not all shapes of constant width cannot be used as wheels for smooth rides (circle is the only one) because even through the width is the same the middle point does not always draw a straight line. I don't know what word you should use but wheel doesn't seem right.
Even-sided coins are going to have the 'hump' rolling past the book edge at the same time on both sides, so the width will change. With odd sided shapes, the hump rolls the edge on one side but there is a flat on the other side. So maybe probably not?
Picture the radius of a round coin. From centre to edge, t's constant. Now picture the radius of a coin that isn't round. The radius from centre to the point of one of the bumps is the maximum radius of the coin (we'll call it X), while the radius from centre to the midpoint of the flat surface between the bumps is the minimum radius. We'll call that Y, and the distance between the maximum and minimum radii is Z. When a coin has an odd number of sides, a bump is always directly opposite a midpoint, so the diameter = the maximum radius (X) + the minimum radius (Y). As we roll the coin off the bump toward the midpoint, on the other side we are equally moving from the midpoint toward the bump, so X decreases at the same rate that Y increases 180 degrees away, and the diameter (X+Y) remains constant. When a coin has an even number of sides, though, bumps are directly opposite bumps and midpoints are directly opposite midpoints. So the length of the diameter between one bump and another is 2Y + 2Z, and the length of the diameter between one midpoint and another is just 2Y. And that's why you get tunka tunka tunka tunka from an eight- or ten-sided coin, but not from a seven- or nine- or eleven-sided one. But even with even-sided coins, the higher the number, the smoother the ride will be, until you get to a circle, which is an infinite number of points.
A shape of constant width can certainly make books slide without bumping but a ride in some sort of conveyance requires an axel. And that axel isn't at a constant distance from the perimeter. Thus, a bumpy ride on such a conveyance is inevitable.
Try this: Construct a chute with two wooden bars. Fix one of the bars on a flat surface. Put a shape of constant width against the fixed bar. Put another bar on the other side of the shape, parallel to the first bar. Make sure that the bars are really parallel. (Two replicates of the same shape work better) Fix the second bar as well. If a shape rotates inside this chute freely but without slack space, It should be one of constant width.
Canada is a pool of softness, niceness, incompetence. Being Canadian is being followers. Only thing Canadians are proud of: we are nicer. If the best thing about a nation is being nice, that's just pathetic. I am Canadian, I am ashamed.
Earthbjorn Nahkaimurrao Damn dude...looked at your channel and your liked videos and playlists are like a bunch of things that I would watch, or like too. Haha
Straylight4299 You could have a radial bearing rolling around in an axle hole of ~similar~ shape, but then you might as well just use the bearing as the wheel.
Before Malta switched to the Euro, several of their coins were non-circular, including octagonal 25c piece and the aluminum 2, 3 and 5 mil coins that were scalloped and could work as little gears.
Constant width shapes still can't be used for wheels because there center moves as it rotates. they can be used as bearings, but you can't put a hub in the middle.
Older Canadian coins had an even more amazing property, in that their value couldn't be as easily arbitrarily determined by a central bank because they were actually made of a precious metal that had market value.
@Steve Mould - Science Videos : Small correction: Canadian Bank Note in Ottawa manufactures polymer notes with their own process. It's based on the Australian process, but it's not the same materials. Almost a year later but, hey.. :)
The reason for the bumps is to be able to tell what coin it is easily from the shape. It helps the blind as well as when fishing (blindly) for change in your pocket, etc.
You say they can work as wheels, is there a way to place the axle so that you wouldn't get a bumpy ride? Also check out 2HK Dollars, what's the reasoning behind that?
+Tom D.H Ah yes, the 2HKD coin. As a HongKonger, I can attest that these coins are designed to be completely useless except for currency. Oh, and it's also easy to pick it out from your coin pouch, and slightly more difficult to forge. But that's really it. There's no crazy mathematical reason behind it or anything.
You don't mean wheel; you mean roller. A log of shapes of constant breadth would work, but a wheel of constant breadth only works if it is circular. I say constant breadth because that's what people used to say when describing this sort of geometry. Width describes negative space (wide doorway, wide opening, wide river), breadth describes positive spaces/solids (broad shoulders, broad pen nibs, etc.). At some point folks got slovenly with their subtle distinctions, and started mixing up the two.
Sadly, these would not work for an automobile. While these shapes do have a constant width, their axis of rotation constantly shifts as they are rotated against a surface. The surface may move relative to the perimeter of the "wheel" along the x-axis and remain stationary along the y-axis; however, the aforementioned surface will vary its y-axis positioning relative to the axis of rotation for the odd "wheel."
It seems to me that you could make a bike wheel out of a shape of constant width if you made the hub large enough to have the inverse shape, so the radius ends up with a constant width. Not sure how you'd put bearings in it, but it's worth a shot.
More about this shape... you can use those shapes to create drill bits that drill polygonal holes. A Reuleaux triangle bit can drill a square hole, for example. A Reuleaux pentagon can drill a hexagonal hole. Google this: drill bit square hole releaux
Constant width is not the same as constant radius which would actually prevent these shapes from giving a car a smooth ride. This kind of shape could function in a sort of 2D ball bearing being the ball, but as a wheel with an axle it would cause a bumpy ride.
Well the main reason these don't work for wheels is that we don't hold wheels from the top, we hold them from a center axis. The only shape with has a non-moving center and a constant width is a circle. They would probably make effective "ball" bearings, though.
I was about to make a "If your coin isn't a shape of constant width you're going to have a bad time" joke but I realised you'd essentially already done that in the video.
No, because the circular wheel has a connection in the middle, and if you did that with the 11 sided coin it would be bumpy, but since the connection was above/bellow the coin as a tangent, it didn't bump. You can't make E.G. a car with a connection as a tangent, if so, the wheel would fall off...
I love how this video is barely two years old and the uk now has another coin that's a shape of constant width and two of our banknotes are now polymer bank notes
You are actually mistaken, the center, or axle if it's a wheel, move and do not stay centered. You can roll them between books, but as wheels, they would not work quite as well as you think.
Anyone old enough to remember the pre-decimalisation British threepenny bit? It too had 12 flat sides and was stackable. Also the UK is introducing a 12 sided pound coin in March 2017, largely for anti-counterfeiting purposes. It will have rounded corners, and is claimed to have acceptable rolling perfomance although it will not have a constant diameter.
Same comment as all the others. Working as a roller or bearing doesn't mean it would work as a wheel. Constant width =/= constant radius. To work as a wheel, you would have to engineer an incredibly elaborate system that rested the weight of the vehicle on the top of the wheel, and had a method to drive them that doesn't use a central axle. Any steering capable wheels would need to be mounted inside a partial sphere, and the slightest piece of debris from the terrain would very likely jam the mechanism. I'd love to see such a contraption actually built, if it's possible, but all things considered, I'm not sure any such resulting system could be defined as a wheel.
+UnknownSquid yeah, I was a bit lose with the definition of a wheel. Someone actually built a bike that works how you describe. I'm on mobile so won't go hunting for a link but search for constant width wheels bike or similar.
*CIRCLES **_ARE_** THE ONLY SHAPE THAT WORK AS A WHEEL* Just a note that at the start you used the term "wheel", and wheels are devices that are used with axels (even the most basic/rudimentary forms). When placed on an axel, a loonie's shape would not give a smooth ride, because they do not have a radius/constant-radius (they aren't a circle). Just because they have equal _width_ does _not_ mean they'd make for smooth wheels. The term that would need to be used to be accurate would be something like "free-standing roller".
The reason why these cannot function as smooth riding wheels is that although the width of the shape stays constant, it's geometric center moves around relative to the ground, which causes it to wabble the axel.
They can't be used as normal wheels because if you put an axle through them then the "radius" will be different as you go around and ride will be bumpy.
Shapes of constant width don't make good rollers either, well if you consider uniform horizontal movement of the platform on the roller. Because such rollers have a centre of mass that moves up and down during a roll.
It would make a great ball bearing, but you could not use them as traditional wheels because though it is an object of constant width, it is not an object of constant distance from the center.
A shape of constant width is always the same distance from the opposite edge. Not from the geometric center, where the axel would be on a wheel. Wheels do have to be circular...
Just having constant width doesn't make a shape good for a wheel. It will roll just fine, but put an axle through the middle of the triangular ones and you're in for a very bumpy ride. The overall width is constant as you roll, but the distance from any point on the edge to the centroid is not constant.
Except wheels are attached at the center, and while the width is constant, the center point is not necessarily so. This works fine is you use rollers instead of wheels (such as rolling it between two books) but not when it's used as a wheel. Interesting video, though - thanks for making it!
I thought the feature would be that they don't roll, so you avoid the annoying coins that roll a km away from you.. also venting machines can still be made so that those coins can roll when inserted.
You do realize, that would NOT work as a wheel? Instead of rolling it between books, try putting an axle through the center, and see how smooth that is.
wheels have to be circles because its the only shape that have equal distance from its center to all sides. it kinda defines circle. wheels made out of ther shapes will be bumpy because you cannot have a place to put shaft on that would make them spin smoothly
Ok but when most people think of a wheel, they think of a wheel-and-axle combination, in which case a circle is the only shape that gives a smooth ride.
Shaped of constant width does not mean smooth ride with that object as a wheel, for the ride to be smooth, there has to be a point (somewhere in the middle) from where the edges are at constant distance, something which circle achieves. constant width just means that diametrically opposite points are at equal width. Please let me know if I am wrong...
Sumeet Singh, I think you have a point. At 1:20 we see that no matter which point we choose as the point at which the wheel connects the axle, the axle will not stay at a constant distance from the ground directly beneath it. This would cause any affixed object such as the body of a car to move up and down like a piston. I'm still in high school so I apologise if I made an mistake.
it wouldn't work as a wheel because traditionally wheels are attached using a point of rotation in the center. In a shape other than a circle, yes there is constant but there is no stationary point of rotation in relation to the surface it is rolling across.
but normally wheels require constant a RADIUS, not the DIAMETER. since typically put an axle through the wheel, a wheel with constant diameter but not constant width will still have a bumpy ride because the relation of the edge of the wheel and the center is always changeing.
