Why are manhole covers round? - Marc Chamberland
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- Опубліковано 12 кві 2015
- View full lesson: ed.ted.com/lessons/why-are-man...
Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there’s another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland explains curves of constant width and Barbier’s theorem.
Lesson by Marc Chamberland, animation by Pew36 Animation Studios.
The reuleaux triangle is used in rotary engines, it spins in the same way as shown in the video. Very cool!
No, rotors in rotary engines from a figure eight path.
Look at the graphic here
en.wikipedia.org/wiki/Wankel_engine
then note that it is referred to as an epitrochoid.
Now look at a definition for an epitrochoid here
en.wikipedia.org/wiki/Epitrochoid
Note that an epitrochoid is formed by rolling a circle around another cirlce (two curves of constant width) forming another shape having a curve of constant width. See 1:48
So after a tiny bit of research on wikipedia and using this video it can be shown that wankel rotors are in fact, curves of constant width (or reuleaux shapes).
Also Im not sure what you mean about a figure eight path, look at the graphic on the wankel engine wiki page, it obviously rotates about a circular path.
The Magic Doritos
Petition to make Rulo Triangle manhole covers.
Boogster Su Where do I sign to put this in my city?
*roleaux, named after the french guy who thought of them i think lol
I would sign that petition!
Haguatchi Franz Reuleaux was a German engineer during the 19th century
Rulo isn't how it's spelt at all. It has an "x" at the end. (it's French.) it has a lot of other differences too.
Also, because when you make a hole sharp corners are weak points, areas or extremely high stress concentrations. While a circular hole is still a stress concentration, it's the lowest of any geometric shape.
+Shivanand Pattanshetti actually, if material a function of perimeter it would be equal. It would take removing less material though.
A Reuleaux triangle also is the heart of a rotary engine.
JaySee5 I thought I was the only one thinking that!
JaySee5 that's the Only thing I was thinking
***** yes, compulsive wanking goes on to propel the car =)
only on the internet...
JaySee5 *I'MMA TELL YOU HOW A ROTARY ENGINE WORKS*
2:25
Partially true. We can indeed make surfaces of constant widths in 3 dimensions but the reuleaux tetrahedron is not one of them. The reuleaux tetrahedron is slightly wider edge to edge than corner to face. Rounding off 3 edges or 3 corners of a reuleaux tetrahedron will however, give you a surface of constant width - this specific occurrence is known as a meissner tetrahedron.
ed.ted.com/lessons/why-are-manhole-covers-round-marc-chamberland under Dig Deeper. You're right and they know it.
Or you could get it by turning a Reuleaux triangle around one of it’s lines of symmetry and the space that it passes through will be a surface of constant width
So pretty much, the answer is:
So the manhole cover doesn't fall in
Correct.
But... the reason it doesnt fall in isnt cause its a circle. it's cause there is a smaller circular suport under it :L Just like metal storm drains and such. A manhole could easily be another shape
Yes, but it wouldn't be much point in making a square man hole cover with a circular support in it, now would it?
Tjita1 Oh. I dont know... maybe you could...
MAKE A SQUARE SUPPORT UNDER IT
Charlie The Cartoonist But if you want to stop the cover from falling into the hole the support has to be smaller than the shortest straight edge of the hole, which as it happens for a square is a circle just smaller than the side of the square.
All this to find out that square manholes covers would fall in...
We actually knew that going in didn't we, plus now we're smarter. Did not know about these other shapes, aside from the Wankel rotary engine, which ironically is a very dumb idea.
bfjb70 I was expecting some special reason.
+Owiko7 Same
In the United kingdom, all the manhole covers, big or small, new or old, are square shaped. In the UK they are all square, without exception. Never, ever, round, always square, billions of them! MANHOLE COVERS IN THE UK ARE SQUARE, NEVER ROUND! So, doesn't that disprove your point, you silly Yanks?
+English Grammar what exactly is the point that you disproved?
why does this channel consistently teach me things that I didn't know that I wanted to learn. ITS SO GOOD
This happens to me too
H O W
Very good example of such an interesting topic. I really hope TED continues to do all sorts of educational videos.
Short answer: So the cover wouldn't fall in
Long answer: Because if you rotate a circle the distance between the bottom edge and the top edge will stay the same distance apart and they could act like a wheel.
What an awesome cartoon story was made for this lesson! I love cartoonist's humour in this one so much! Wise and intelligent caveman teaches geometry, riding a board, and that funny fall down into square hole. Great job!
Eureka...I have already known that other shape of manhole cover, such as triangle, square, and etc, could fall in, but the concept of curve of constant width.... is something new to me... Thank Ted-Ed...you are my great teacher...
Спасибо. Как всё просто, когда объясняют кратко и только суть. Удачи вам.
I love those kind of topics. Thanks Ted-Ed :)
I paused an episode of my favorite show to watch this, because... manhole covers! Why _are_ they round?
Great video! I love the theorem behind Reuleaux polygons.
Great video, learned way more from this than I'd expected to. Thanks.
Really loved the ideas shared in the video👍
I'm doing this as my science fair and it helped me sooooooooooooooooooooooooooo much thank you for this amazing video.
Someone said that it would be easier to just say "so they can't fall through the hole."
- showing us exactly how the science IS taught at schools instead of how it SHOULD be taught.
I can’t tell- are you saying TedEd is wrong for being roundabout in their answer or the person is wrong for just wanting the answer and not wanting to learn.
Maybe this guy was not taught English effectively?
@@nation5743 He is saying that somebody else suggested the video can be summed up as 'it can't go in the hole". He then went on to suggest that schools simply tell you that it can't go in the hole instead of explaining why.
It's really not complicated, he made perfect sense.
the sky is blue because i said so
You do know that now you know more than you came for? this is way better, don't keep blaming schools
Is it just me or did 2:56 look extremely violent?
It's just you
It's not violent it looked painful
Just you
Hmmm... looks familiar
+Modus Operandi your profile pic fits well
Indeed, wonder where I've seen it
Modus Operandi is it present in the RGB Reuleaux Triangle diagram?
Ivan IV the Terrible wankel/rotary engine
The Magic Dorito!!
Now I hope they change all the manhole covers into those other shapes! :-)
That was great!
I love topics like this.
This is such fluid animation
I was putting this episode off until I had nothing interesting to watch. This video was far more informative than the title suggested. It's like anti clickbait. Thanks for the surprise.
The video explained in depth WHY a shape like a circle wouldn’t fall on, then showed you the practical application
And they say maths is useless
A manhole is made of two parts. The manhole cover and the frame it sits in. The frame has an inner lip which the cover or lid sits in. The actual diameter of the lid and the concrete tubes which are stacked on top of each other may be the same diameter but the lid itself will never fall through the frame.
Exactly. The hole isn't just one diameter and its never a friction fit like is show in the video. The counter bore of the hole, or the "lip" so to speak would allow any shape to work. The whole argument for it needing to be constant width completely ignores the real world application of manhole covers.
@@timothymantor7332 If you don't want the lip to have to be huge though, the shape needs to be of constant or near constant width. If you had a square manhole cover, for example, it could fall through the diagonal unless the lip is huge (at least (sqrt(2)-1)/2 ≈ 0.2 times the side of the cover. So if it was 1m wide, you would need a 20cm lip on each side )
Love the animation.
this is an interview question: Production costs would be my answer.
consider we need a hole 2 feet in diameter:
a square would be 4 sq/ft: 2 w x 2 L = 4
now a circle's area is pi r squared :
if diameter is 2 feet, then radius is 1/2 = 1 foot
pi(rounded) 3 x (radius) 1= 3 sq/feet
so you save 1 foot of production, distribution and labour
plus, the squares have a hinge which raises production costs.
Is the math above correct?
thanks for this video!
1) I like the animation. Well done and a good way to break the norm.
2) what if we had a Rulo-triangle wheel? How would that work out? Better or worse then our current tires? Would it save on materials needed to make the tire/wheel?
Although it has a smaller area, the pointy bits are weak points
I knew the answer to the original question, but the rest of the video was way more interesting than the answer. Cool.
I dont allways comment on a youtube video, but when I do, I do it because I am quite impressed.
cheers-.
Learn something new every day
Don't tell me what to do!
thanks,you cleared my doubt.
Would an equilateral triangle fall in though? With other polygons you can fit an edge between two opposite vertices, but an equilateral triangle's edges are the lines between opposite vertices.
With an equilateral triangle you can fit its height inside a base
Rotary engine
This is fascinating. Is there an advantage of a Rulo triangle over a circle in this case?
+Antony C Less area which means less material needed to create one
+roxyvaseline Very, very true. But it would require trial and error since they have to get the size exactly right
Excellent!
nice explanation
"Ruleaux tetrahedra" are NOT solids of equal width. There's a bit on the corner edges that over laps. The actual analogue that does work is bounded by a fifth, much smaller sphere in the middle. Another one looks kinda like an 'egg bullet'.
Oh hey, Numberphile did a video on surfaces of constant width!
Well that ending was rather dark.
Legend has it that the caveman is still down there.
I think the Reuleaux tetrahedron is *not* a constant width surface.
I love this speaker
So turtle shells can fit through them?
The thing about curves of constant width is that the length isn't constant exept circles that's why manhole covers are circles and not some other shape that has the property "curve of constant width"
We should make Reuleaux triangle manholes. #ReuleauxManhole
Everyone seems to over look this important detail. The circles can fall through there holes, which is why it sits on a ledge, so ultimately it they chose a circle to sit on ledge then a square because they would need bigger ledges for it to rest on and not fall in. So to sum it up, the answer as to why man hole covers are round is because it's more convenient for everybody.
That's a fine reason.
reuleaux tetrahedron is Not a surface of constant width, go search it
that title belongs to meissner tetrahedra which is modified from reuleaux tetrahedron
The rulo triangle is a guitar pick
Is it just me or was anyone else thinking about rx-7s after they brought up the reuleaux triangle?
Why, it's a Toblerone-Rolo combo!!
(read in heavy Geordie accent)
Only at the very end did the video tell you why manhole covers are not square. Manly talked about Rulo Triangles not manhole covers! It was interesting though!
Hey what about circular rectangle
does anyone else wonder about the idea of useing the rulo tetrehedrea as surfing power. Cause I realy want to do that.
for a reuleaux polygon the shape must have odd number of vertices and since circle is a reuleaux polygon with infinite vertices dose this means circle has odd number of vertices i.e. Dose this mean infinity is an odd number??
wowzer
As you can see with the polygons, as the number of sides increases, the length of these sides decreases until such an extent that these sides are too small to be seen and from a distance, the polygon with very many sides looks like a perfect circle.
It's not that infinity is odd, its just that there is relatively not much of a difference between a polygon having N sides (N being a very large number) and a polygon with (N+1) sides. Surely, one of these shapes have an odd number of sides. But because of the very small lengths of the sides, there is but, an infinitesimal* difference. The difference is so small, it almost doesn't matter anymore.
The beauty of the circle seen here is that the number of its sides is too large and therefore described as infinity but we cannot even imagine the exact number and this can be thought of as either even or odd.
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infintesimal is the opposite of infinite : it is used to describe very small numbers (ex: 0.00000...more zeroes...000001 is an infinitesimal number)
*Question* : what about *Equilateral triangle* ? They shouldn't fall in, should they? if so, how?
Yousuf Azad Sami They don't. But good luck rolling it!
The height of the triangle can fall in through a base
to put it more simply a circle wont fall down its own hole
HAHAHAHA the cave man falling through the square killed me
Uhm...So I'm kinda worried about the guy at 3:11, couldn't TEDEd have gotten him out or something...
Reuleaux any-shape-with-odd-number-of-sides manhole cover? Ok! (Reuleaux shape are ROUND as well, but not spherical)
One of interview questions
The rotary motor....
I tried doing this with a square... just keep getting a circle
cool!
Why does the rulo triangle work? I’m very confused.
Ok, I think I just made a Roleau square with my compass, how is this posible?
the when the orange suit man falls in the manhole there will be a sound and that is so funny
3:12 have anyone come across a Reuleaux triangle manhole yet? Say hi to that poor caveman :-)
Don't these shapes also distribute pressure evenly from cars passing over?
im confused about the reasoning at 3:02 because squares are like the only shape that can fall through the hole they make. equilateral triangles cant, right pentagons cant, right hexagons cant, right heptagons cant and the list goes on...
Those shapes all can. the height of equilateral triangles can fall through the base, and with any "right" shape a shorter diagonal can fall through a longer one.
If a shape isn't of constant width, that means at some points it will have more width and at others less width, and so the parts with less width can fall through the ones with more width
you can put on a circular manhole at any angle, so yeah
My town has square man hole covers for some reason…
They used the triangles for good engines
wow!
Moral of the story: Cavemen are still alive and are just trapped in reuleux triangle manholes across the world.
Car Guys: THE MAGIC DORITOOOO!!
There was a space between our beds and when I was 5-? years old , I called it a manhole.
lol gotta love the caveman animation!
I was wondering why some watches are shaped like this.
we have square man holes here in our subdivision.
More like these
Here in Vietnam we always have squared concrete manholes. Guess bc of the expense reason
... same with some other asian countries as well
But the Reuleaux tetrahedron doesn't have constant width. You're thinking of the Meissner tetrahedron.
...how in the hell did TED Ed make shapes so interesting?
CGI Ted Ed.
What is next?
The CGI style looks familiar, reminds me of "The Croods" movie. Same animators?
1:20 - o.O (Amaterasu! - R.I.P. Itachi)
I gasped when the caveman fell in the whole. Really surprised me with that one
And you call yourself a teufel...
+Anthony Nichols -- You mean he fell in a hole.
I prefer to call it a plectrum
Yhh, the animation...
2:24 he invents rulotetrahedron and just walks away!!!
Now we know how Tri-beams make square holes.
Google interviews asked this question.
but in England we have square and rectangular ones.....
In Germany we have them too
Well, this video is very incorrect xD
why the hands are so big
Now I wonder the math of mastermorphix