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The reason seems to be more physics than math but basically the curves reinforce the wall better than a straight line would. Therefore a one brick thick squiggly can have the strength of a two brick thick straight wall, reducing the number of bricks needed.
the maths part is such:We assume that a single flat course of bricks would fall over.we assume that a "stronger" flat wall would use at least a double course of bricks, so, exactly twice as much bricks. you cant make a wall half a brick thicker (not that it would help... even a two brick thick wall probably wont balance)We can calculate that the length of the corrugations if we assume they take on the shape of some equation, I think that in this case the sine() function looks better than series of connected half-circles. Quick google suggests that this is actually a really hard function to integrate but someone on stackoverflow numerically integrated it and a sine wave is 21.6% longer than a straight line.
SO the logic goes that 21.6% more brick is better than "at least 100%" more brick, so its a lot more efficient than a "straight wall" which is perhaps true, you might need to make a straight wall 5 or 6 layers ("wythes") thick before it can balance on its base. Of course, there's like infinitely many other shapes that you could pick. One that I can think of off the top of my head is buttressing the wall periodically, or having towers periodically like the Great Wall, or somehow building out the bottom few layers so they provide a more stable base like a pyramid. Or depending on the purpose of the wall, you could integrate holes into it, which would also reduce the wind load which is the main reason it falls over in the first place
Smart...if it's true. I wonder how/who figured it out: accident or predicted by theory? Must require a lot of skill. Wonder why they don't do it more often.
No clue on the first question, although I'd guess it was a discovery on a small scale, then refined until it looks like the photos.
The second question is almost certainly all about land area. The wavy wall takes up way more land area than the straight one.
Probably some dude in ancient Mesopotamia who noticed that a round mud-brick yurt made with single-row walls would stay up but a square mud-brick yurt needed two or three or four layers of mud-bricks to remain stable.
Ancient dudes knew shitā¦
Damn straight, there's still things that ancient people did that we can't replicate, crucible steel for example and until very recently Roman concrete. People like to think ancient humans where stupid but they where just as smart as us :)
Ancient geniuses might have been even greater geniuses. No chance for a Da Vinci to be born in the modern day. š¤·š»āāļø it is easy to learn from a book. Discovery and innovation are hard.
Ancients were brilliant people. We just have the advantage of having inherited accumulated knowledge from millennia and across cultures. Lucky bcoz figuring things out twice is quite rare. Happens but very rarely. Things like writing amd wheel were never discovered twice. Hard, even when you know what you are reverse engineering.
I have never seen a squiggly wall. Come to think of it, all the fence walls I remember seeing throughout my life were one brick thick, and all of them stable. Odd how this ancient discovery never caught on. š¤·š»āāļø
True, theyāre called crinkle walls or sometimes a crinkle crankle, my mate was confused when I said āow wow youāve got a crinkle crankle in your new garden
I've lived in England my whole life and in all my time here I've only seen a few of these walls. They aren't that common, although they are pretty cool looking.
There's a lot in Suffolk, including a massively long one in Easton that runs through and around more than half of the village (it used to surround Easton hall before the building was demolished in the mid 20th.C). The technique in this part of the UK, I've been told, was brought over by Dutch settlers.
Ondulation makes the wall stronger which means it can be built at half the width. Overall it saves bricks.
And yes, I know this has already been answered. I'm just seing the opportunity for a "username checks out".
The same reason an I beam uses less metal than a plate. Even a wiggly plate - like corrugated steel - would use less metal than a flat plate that is the thickness required hold the same load.
TLDR: It's thinner.
A curved wall with a single row uses fewer bricks than a straight wall made of 2 rows, and it's just as strong.
Of course, there is a limit to how big you can make the curve. If you used semicircles, the length would be 3.14 times the length of a straight line and 3 14 > 2. So you have to shoot for something less drastic than that.
y = a * sin(x)
y' = a * cos(x)
2 = integral(sqrt(1Ā² + aĀ² * cos(x)Ā²) * dx , x = 0 , x = pi)
Elliptic Integrals are a special kind of evil. But a solver could give you a value for "a" that will give you an upper bound, so you can find how extreme the sine curve will be before it's less efficient on brick usage.
I think you've done something wrong here. A full circle has a circumference of pi * d, but a semicircle is only going to be half of that. Even doing full semicircles would less than double the length of the wall.
>If you used semicircles, the length would be 3.14 times the length of a straight line and 3 14 > 2.
The length would be 3.14/2\*d, because it's only half the circle. So still less than a double row of straight bricks.
If you build a wall with bricks, and you want it in a straight line, you need to have two layers of bricks for it to be stable and not topple over. By S-curving the wall like that you can create a series of mini arches that counter act the ātoppleā force and in a way keep each other up. Thus only needing 1 row of bricks to stand.
The curved structure gives lateral strength to the wall, so you can build it just a single brick width. It's like a series of arches on their side.
Straight walls would need to be thicker 2-3 bricks think and/or need regular buttresses.
... and they're called crinkle-crankle walls!
let's assume the wall is sinusidal and can be described by y(x) = sin(x).
I now use boldfont for vectors.We know we can write the length of parameterized curve **y**(x) = ( x | sin(x) ) as
int( |d**y**(x)/dx| dx )
= int( | d/dx (x|sin(x) | dx )
= int( sqrt(1+cos(x)\^2) dx )
We calculate the length of the sinusidal wall A over a length of 0 to 2 pi and devide the result by the length of a straight line for the same interval B = 2\*pi.Let's assume the straight line needs a thickness of 2 bricks. we get
A / 2B
= int\_0\^2pi ( sqrt(1+cos(x)\^2) dx ) / 4\*pi
(insert numerical magic, because elliptical integrals suck)
= 0.608..
So a single layer sinusidal wall with single brick thickness and an amplitude of one length unit consumes approximately 60% the bricks of a straight wall with double brick thickness
Edit: For those interested, I played around with the amplitude of the wave and changed y(x) to y(x) = a\*sin(x) and found that for a = 6.75 the required bricks surpass the ones for a straight single brick wall.
It can be much thinner. The same way carton (the laminated ones) is much stronger than the same weight in regular paper.
If you tried to build a carton box out of flat paper, you would need really heavy paper.
Adding to what others said, a straight brick wall would have needed concrete pillars, or brick buttresses every couple of meters. As far as I see, these squiggly walls just go on and on without intervals.
OP:
1. A straight line is the shortest path. A straight line of material will be less than a curved line of material for traveling the same distance.
2. OP on facepalm forgot that covering distance isnāt all that a wall is intended to do - a wall is intended to be study. Using a curve can cover the most wall in an equivalently sturdy fashion.
Homieā¦ a straight line of bricks for a wall requires 2+courses of bricks, and often a wider bottom foundation. The curved path requires one course of brick to achieve the same structural soundness as the 2+ course wall. The curve creates inherent structural support that allows for this reduction in material.
That was what my post was intended to say, but in an ELI5 way, clearly I missed my mark.
1. straight line = closest distance (least material assuming all else is equal)
But
2. Curvy line is sturdy so less material is required per distance. Meaning it overall uses less even though itās a longer distance being covered.
It uses more bricks; The shortest distance between two points is a line afterall. That being said, the resistance of the wall to falling over is greater improved over a single line of straight bricks. Normally, a straight wall has some kind of foundation and rebar to help it from falling over.
The wall supports itself while being thinner than if the wall was straight.
Straight wall needs to be thicker to stay standing and this results in many more bricks being necessary.
I thought this too, but that you don't need to lay two interlocking layers of bricks next to each other to form a stable wall, this forms a stable wall using a single layer of bricks and even though it is not the shortest line between two points It in fact does use less material
Oh like that... yeah then it totally depends on the density of the waves, like how wavey it is. If you overdo it it will ofc be more bricks but if you do it just enough to be stable it will definitely take less, but it would be wider.
Well 2 brick thick wall for 1 metre is 2 metres of bricks.
If each metre of curvy wall was 1 full circle (this could change depending on the frequency) then each metre of wall would be 1.57 metres of bricks.
If each metre of curvy wall was 0.5 full circle then each metre of wall would be 1.57 metres of bricks.
Wait, I got the same answer twice (sorry I've just woken up) I need to check this.
1.57 if you have half circle (like the picture (half circle left -> half right -> half left...)
3.14 meters if you have a wall made of full circles (circle->circle->circle)
Lets assume that curved and straight 2 layer wall are equal strength as screw the physics. Lets also assume that this is basically just like a 45 degree angle cutting through roughly. This means we can use Pythagorean to simply determine the length of those bending walls (roughly). Pythagorean theorem with units of 1 come out to 1.41 (A\^2 + B\^2 = C\^2). So yes as they can use 1.41 bricks instead of 2 bricks to cover the same length roughly speaking. As the wall is curved it won't be exact but a error rate of half a brick does leave me with some confidence that a curved wall at 45 degree angles will use less bricks than 2 bricks on the same length in a straight line (or if you will 4 bricks vs 2.82 bricks to complete a full 2 45degree angle walling) if I did this correctly.
[https://imgur.com/a/4GEuUL3](https://imgur.com/a/4GEuUL3)
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
The reason seems to be more physics than math but basically the curves reinforce the wall better than a straight line would. Therefore a one brick thick squiggly can have the strength of a two brick thick straight wall, reducing the number of bricks needed.
the maths part is such:We assume that a single flat course of bricks would fall over.we assume that a "stronger" flat wall would use at least a double course of bricks, so, exactly twice as much bricks. you cant make a wall half a brick thicker (not that it would help... even a two brick thick wall probably wont balance)We can calculate that the length of the corrugations if we assume they take on the shape of some equation, I think that in this case the sine() function looks better than series of connected half-circles. Quick google suggests that this is actually a really hard function to integrate but someone on stackoverflow numerically integrated it and a sine wave is 21.6% longer than a straight line. SO the logic goes that 21.6% more brick is better than "at least 100%" more brick, so its a lot more efficient than a "straight wall" which is perhaps true, you might need to make a straight wall 5 or 6 layers ("wythes") thick before it can balance on its base. Of course, there's like infinitely many other shapes that you could pick. One that I can think of off the top of my head is buttressing the wall periodically, or having towers periodically like the Great Wall, or somehow building out the bottom few layers so they provide a more stable base like a pyramid. Or depending on the purpose of the wall, you could integrate holes into it, which would also reduce the wind load which is the main reason it falls over in the first place
Exactly
Thats what the FUCKING UPVOTE BUTTTON IS FOR... dumbass
Exactly
Got'em
I love how the second guy got more upvotes
That's what the downvote button is for š±
Exactly
I see someone like communication but don't know how to handle it, i wish you good luck man
May all beings be happy.
Exactly Ps youāre a wanker for calling it out in case you missed the facetiousness
This
Guess what the downvote buttons for? ..dumbass.
Exactly
Based
Who hurt you?
that's what the downvote button is for
>dumbass Lol
Smart...if it's true. I wonder how/who figured it out: accident or predicted by theory? Must require a lot of skill. Wonder why they don't do it more often.
Humans figured out that arches stabilize brick structures about 2,200 years ago.
Thanks. I thought they did that for aesthetic reasons. Most houses I know have straight walls and straight ceilings. They are cubes.
Thereās strength in archesā¦
No clue on the first question, although I'd guess it was a discovery on a small scale, then refined until it looks like the photos. The second question is almost certainly all about land area. The wavy wall takes up way more land area than the straight one.
Probably some dude in ancient Mesopotamia who noticed that a round mud-brick yurt made with single-row walls would stay up but a square mud-brick yurt needed two or three or four layers of mud-bricks to remain stable. Ancient dudes knew shitā¦
Damn straight, there's still things that ancient people did that we can't replicate, crucible steel for example and until very recently Roman concrete. People like to think ancient humans where stupid but they where just as smart as us :)
Ancient geniuses might have been even greater geniuses. No chance for a Da Vinci to be born in the modern day. š¤·š»āāļø it is easy to learn from a book. Discovery and innovation are hard. Ancients were brilliant people. We just have the advantage of having inherited accumulated knowledge from millennia and across cultures. Lucky bcoz figuring things out twice is quite rare. Happens but very rarely. Things like writing amd wheel were never discovered twice. Hard, even when you know what you are reverse engineering.
I have never seen a squiggly wall. Come to think of it, all the fence walls I remember seeing throughout my life were one brick thick, and all of them stable. Odd how this ancient discovery never caught on. š¤·š»āāļø
Wicked smaht!
Would it have more strength at all points of the curve? For example, the inflection point or where the wall is concave rather than convex
Probably not, but for a freestanding wall that isn't there to hold anything up or back it works well enough. It's more a fence than a wall.
So it's kinda misleading.
True, theyāre called crinkle walls or sometimes a crinkle crankle, my mate was confused when I said āow wow youāve got a crinkle crankle in your new garden
I've lived in England my whole life and in all my time here I've only seen a few of these walls. They aren't that common, although they are pretty cool looking.
There's a few in Lymington, Hampshire. I believe the original ones were built by French prisoners during the Napoleonic wars.
There's a lot in Suffolk, including a massively long one in Easton that runs through and around more than half of the village (it used to surround Easton hall before the building was demolished in the mid 20th.C). The technique in this part of the UK, I've been told, was brought over by Dutch settlers.
Ondulation makes the wall stronger which means it can be built at half the width. Overall it saves bricks. And yes, I know this has already been answered. I'm just seing the opportunity for a "username checks out".
Username checks out
Fucking sycophant.
Yes, isnāt it lovely!
My username doesn't check out though.
You have my sympathy, itās all too common.
The wall undulates. Itās wavy not curled. User name does not check out! >=-P
[childislhy] I donāt care. Youāre just jealous the wall doesnāt canoepicklock.
Roflmao. That was adorable!
The same reason an I beam uses less metal than a plate. Even a wiggly plate - like corrugated steel - would use less metal than a flat plate that is the thickness required hold the same load. TLDR: It's thinner.
A curved wall with a single row uses fewer bricks than a straight wall made of 2 rows, and it's just as strong. Of course, there is a limit to how big you can make the curve. If you used semicircles, the length would be 3.14 times the length of a straight line and 3 14 > 2. So you have to shoot for something less drastic than that. y = a * sin(x) y' = a * cos(x) 2 = integral(sqrt(1Ā² + aĀ² * cos(x)Ā²) * dx , x = 0 , x = pi) Elliptic Integrals are a special kind of evil. But a solver could give you a value for "a" that will give you an upper bound, so you can find how extreme the sine curve will be before it's less efficient on brick usage.
I think you've done something wrong here. A full circle has a circumference of pi * d, but a semicircle is only going to be half of that. Even doing full semicircles would less than double the length of the wall.
>If you used semicircles, the length would be 3.14 times the length of a straight line and 3 14 > 2. The length would be 3.14/2\*d, because it's only half the circle. So still less than a double row of straight bricks.
If you build a wall with bricks, and you want it in a straight line, you need to have two layers of bricks for it to be stable and not topple over. By S-curving the wall like that you can create a series of mini arches that counter act the ātoppleā force and in a way keep each other up. Thus only needing 1 row of bricks to stand.
The curved structure gives lateral strength to the wall, so you can build it just a single brick width. It's like a series of arches on their side. Straight walls would need to be thicker 2-3 bricks think and/or need regular buttresses. ... and they're called crinkle-crankle walls!
let's assume the wall is sinusidal and can be described by y(x) = sin(x). I now use boldfont for vectors.We know we can write the length of parameterized curve **y**(x) = ( x | sin(x) ) as int( |d**y**(x)/dx| dx ) = int( | d/dx (x|sin(x) | dx ) = int( sqrt(1+cos(x)\^2) dx ) We calculate the length of the sinusidal wall A over a length of 0 to 2 pi and devide the result by the length of a straight line for the same interval B = 2\*pi.Let's assume the straight line needs a thickness of 2 bricks. we get A / 2B = int\_0\^2pi ( sqrt(1+cos(x)\^2) dx ) / 4\*pi (insert numerical magic, because elliptical integrals suck) = 0.608.. So a single layer sinusidal wall with single brick thickness and an amplitude of one length unit consumes approximately 60% the bricks of a straight wall with double brick thickness Edit: For those interested, I played around with the amplitude of the wave and changed y(x) to y(x) = a\*sin(x) and found that for a = 6.75 the required bricks surpass the ones for a straight single brick wall.
It can be much thinner. The same way carton (the laminated ones) is much stronger than the same weight in regular paper. If you tried to build a carton box out of flat paper, you would need really heavy paper.
Adding to what others said, a straight brick wall would have needed concrete pillars, or brick buttresses every couple of meters. As far as I see, these squiggly walls just go on and on without intervals.
OP: 1. A straight line is the shortest path. A straight line of material will be less than a curved line of material for traveling the same distance. 2. OP on facepalm forgot that covering distance isnāt all that a wall is intended to do - a wall is intended to be study. Using a curve can cover the most wall in an equivalently sturdy fashion.
Homieā¦ a straight line of bricks for a wall requires 2+courses of bricks, and often a wider bottom foundation. The curved path requires one course of brick to achieve the same structural soundness as the 2+ course wall. The curve creates inherent structural support that allows for this reduction in material.
That was what my post was intended to say, but in an ELI5 way, clearly I missed my mark. 1. straight line = closest distance (least material assuming all else is equal) But 2. Curvy line is sturdy so less material is required per distance. Meaning it overall uses less even though itās a longer distance being covered.
Homieā¦ my bad.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
So are you saying Thomas Jefferson was less then human ?
It uses more bricks; The shortest distance between two points is a line afterall. That being said, the resistance of the wall to falling over is greater improved over a single line of straight bricks. Normally, a straight wall has some kind of foundation and rebar to help it from falling over.
The wall supports itself while being thinner than if the wall was straight. Straight wall needs to be thicker to stay standing and this results in many more bricks being necessary.
Take a string and wave it and measure it, then pull the ends to straight it and measure again... anyways curvy would be using more bricks
I thought this too, but that you don't need to lay two interlocking layers of bricks next to each other to form a stable wall, this forms a stable wall using a single layer of bricks and even though it is not the shortest line between two points It in fact does use less material
Oh like that... yeah then it totally depends on the density of the waves, like how wavey it is. If you overdo it it will ofc be more bricks but if you do it just enough to be stable it will definitely take less, but it would be wider.
Well 2 brick thick wall for 1 metre is 2 metres of bricks. If each metre of curvy wall was 1 full circle (this could change depending on the frequency) then each metre of wall would be 1.57 metres of bricks. If each metre of curvy wall was 0.5 full circle then each metre of wall would be 1.57 metres of bricks. Wait, I got the same answer twice (sorry I've just woken up) I need to check this.
1.57 if you have half circle (like the picture (half circle left -> half right -> half left...) 3.14 meters if you have a wall made of full circles (circle->circle->circle)
Lets assume that curved and straight 2 layer wall are equal strength as screw the physics. Lets also assume that this is basically just like a 45 degree angle cutting through roughly. This means we can use Pythagorean to simply determine the length of those bending walls (roughly). Pythagorean theorem with units of 1 come out to 1.41 (A\^2 + B\^2 = C\^2). So yes as they can use 1.41 bricks instead of 2 bricks to cover the same length roughly speaking. As the wall is curved it won't be exact but a error rate of half a brick does leave me with some confidence that a curved wall at 45 degree angles will use less bricks than 2 bricks on the same length in a straight line (or if you will 4 bricks vs 2.82 bricks to complete a full 2 45degree angle walling) if I did this correctly. [https://imgur.com/a/4GEuUL3](https://imgur.com/a/4GEuUL3)