Julian Emil Santos What about gates? Yeah, you could make rounded gates too, but why not make it simple and make one or two sections of the wall just rectangular if only to have a decent gate?
Technically, every part of a circular wall is a weakpoint. Just like an encircled enemy, each section of the wall would met with the maximum number of attacker per perimeter length . Add to the fact that cannons work best in transfering its energy if it hit a wall at or about 90 degree angle, compared to a straight wall, every cannon that surround a circular wall would be capable to hit it at straight angle no matter where they are. This is part of the reasons why star forts are developed.
You missed a few things... Living in a circular city, you have less travel time to get to more places. This means you can more easily defend the walls, and citizens can get to and from their houses, jobs, and/or markets faster, leading to a better defended, more prosperous city.
:( you got us, most of our modern cities are generally in squares for simplicity of roadways, we really don't have to worry about defending our borders all that often anymore, just every once in a while
Andrew Having utilities in a grid format is so much easier... Circles make everything so much more difficult... As for defending your borders... Isnt that what the Alamo was for? Wink Wink
@@olemew Round things stabilize themselves by their shape. Eggs, for example. If you try to crush an egg with your fingers at the two ends furthest apart, you will find it very difficult. The pressure is distributed by the shape on the shell and it remains stable. This also applies to other things with a round shape. Other examples are balls, domes on buildings, or even walls to some extent.
@@eg-qv9ys Domes were used because they create open spaces and have religious symbolism, not because they were stronger against external forces. City-walls would never be crushed like an egg. Therefore, I still don't see how they are "stronger" or against any kind of stress (wind, catapults, etc.)
It should be noted that your super round example in Germany is built in the impact crater of an ancient asteroid. They just built the wall according to the natutal terrain of the crater. BUT the asteroid and it's creater are both round because of the reasons you stated.
The last tangle problem isn't correct... You pick random points on red line and blue line, how will you ensure that the circle passes through these random points? Also we need to make sure that the the circle cuts the triangle in equal areas... And what is the centre of that circle?
I didn't get the problem and its solution. If the curve we are looking for is a circular arc then the 2 starting points could not have been picked at random.
Think of all the curves connecting a red dot and a green dot. We only consider the curves that divide the area of the triangle in half. The question: which of these curves is the shortest. It ends up that the circular arc is the shortest.
Yes, but only if I have picked the 2 dots to be in specific places on the edges. If I have picked the 2 dots near the point that the red edge and the green edge intersect then the circular arc does not divide the triangle area in half. In this case another curve has to be picked as the shortest which do divide the area in half.
The argument in the video works no matter which green point and red point you choose. Remember, though, that the curve has to cut the area of the triangle in half. Even if the two points are close, you can always construct a curve that bisects the area.
+Tipping Point Math I have to say I'm confused about that part as well. When you change the blue shape to a circle, the green dots you chose earlier change position. Is that because that's just what we're trying to find here? The two points that give us the shortest possible curve that cuts the triangle in half?
Yes, we are trying to *show* that the appropriate sized circle is the shortest path that connects the green edge to the red edge while cutting the triangle into two equal-area regions. We are not assuming that the red and green points are fixed.
+Khalid M. Adel i just dont get it what happens when i choose two dots near to the intersection of red and green it would then make a tiny circle and how is its area 50% of the whole thing
Because you need "jagged" walls and towers so that there are no blind spots for defenders. Imagine attackers walk up to a circular wall. The only danger they can expect is from directly above their heads. If the wall doesn't have hoarding or whatever it's called, they are completely safe and can start digging under the wall. Other examples in this video aren't bad, but that Nordlingen city doesn't even have proper towers. But they probably had some other reason to build it that way.
That’s the filming location for kings landing, also many other filming locations are in different parts in Croatia, I live in Northern Ireland where the most filming took place which is pretty cool. 😎👌💯
It's quite simple to imagine volumetric structures of strong triangular form for practical purposes that are already exist such as roofs, tents, bridges , communication towers, geodomes, etc. The main aspects of reasoning would be: biological (sharp edges are unsafe/inconvenient, strict angles are alarming/threatening) and physical (overcomplicated building with optimal-sized instruments and resources is expensive). Otherwise, it is more appropriate to study superiority of triangular shapes in dynamic mechanisms or systems to increase theirs efficiency (e.g. reuleaux triangle, ternary computer, triangular screw). Also, triangular furniture and clothing are rather beautiful...
Do some actual research please. A semi circle is as big as a full circle of the same parameter. The reason is the present of the coast. Also a curve through six points is generally not a circle. It's only a circle if both your starting and finishing point are mid points. Look at the change from the raw blue region to the circle, the points are moved. Busted.
+Xuan Bach Lai you can actually choose two points so that when you replicate the triangle you get a circumference with radius R which bisects the resulting hexagon area
+Xuan Bach Lai and how is a semicircle as big as a full circle? Perimeter_Area for each shape: 2PiR _ PiR^2 for the full circle (Pi+2)r _ Pi(r/2)^2=Pi(r^2)/4 (i) for the semicircle Equal perimeters: 2PiR=(Pi+2)r => R=r*[(Pi+2)/(2Pi)] Substituting R in the full circle area: Pi(r^2)*[(Pi+2)^2]/(4Pi^2)= [Pi(r^2)/4]*[(Pi+2)^2]/(Pi^2) (ii) Dividing i and ii by Pi(r^2)/4 and comparing both: 1< [(Pi+2)^2]/(Pi^2) So the full circle is bigger even if it has the same perimeter. Trivial.
Ok, my bad on the semi-circle one. I messed up. But about the bisecting thing, what I meant was that 2 random points on an 60 degree angle and a circular arc, copied 6 times, would not make a full circle. And no, there are cases when no circumference can satisfy because it would not fit into the triangle.
Just in the early ages of fortified cities you can find a circular shape of walls. Most common shape in medieval and renaissance walls is the star. A star shape is the opposite of your theory, and its the quintessential defensive structure shape in those ages.
the walls are not like a rope that you have to stretch to find the better shape, you literally build it in the shape you need to surround your city or the shape that give you advantages on defence during sieges. The only advantage in round shape is a lower use of materials needed to go around the city, but if a city is rich and has no lack of stone the engineers will chose a star shape, because when you build a fortification the only important thing is the defense strenght, and a round shape is probably the worst kind of fortification.
en.wikipedia.org/wiki/Bastion_fort this is the wikipedia page aobut the italian fortification ("Fortificazione alla Moderna" in Italy) it says the complete opposite of this video about the shape of ancient walls.
AGAIN, STAY TUNED FOR MORE VIDS BY CAPTAIN OBVIOUS INCLUDING: 1) Why water runs downhill. 2) Why wood comes from trees. 3) Why eating makes you poop 4) where babies come from. 5) Why dogs don't meow 6) Why basements are not attics. 7) Why the rain doesn't fall up. 8) Why it gets dark at night ...and MUCH MUCH MORE!
WHY ARE WALLED CITIES ROUND? REALLY? That's a subject? First, that's a falsehood being that it's not near 100% true. (Google town walls / Images) So WITHOUT watching the vid, let me save you the trouble. The first building goes up in a most desirable location; everyone likes desirable locations, so they become neighbors on the next-to-most-desirable land. Tradingpost, church, bar and townhall follow near center and now you're on your way to City-hood. Now, since it's true, most towns spider web in all directions once established, yeah round, which is priority for protecting, THUS the wall's dimensions. NO MATH INVOLVED that's tougher than 1+1, folks ...Maybe you should produce a Vid on why holes get bigger when you keep digging in the same space. ...or maybe a Vid on why the simplistic gravitate toward TH-cam to simulate creativity with the most obvious of content. ...NEXT.
Oh, come on. Can't ya take a joke? Actually, I'm just sticking around because I'm waiting for the follow-up, "Why tall buildings are called sky-scrapers". the suspense is killing me. -DW
To keep titans out, duh
Ahhhh our people is here😌. shinzou sasageyo!!!
Lol
EREN YEAGAH
😐
69 likes. Nice.
Also, there's no "weak point" in the circular wall. All parts of the wall are equidistant from the center.
Julian Emil Santos
What about gates? Yeah, you could make rounded gates too, but why not make it simple and make one or two sections of the wall just rectangular if only to have a decent gate?
true. i can agree that you can sacrifice the wall shape for better security
Technically, every part of a circular wall is a weakpoint. Just like an encircled enemy, each section of the wall would met with the maximum number of attacker per perimeter length .
Add to the fact that cannons work best in transfering its energy if it hit a wall at or about 90 degree angle, compared to a straight wall, every cannon that surround a circular wall would be capable to hit it at straight angle no matter where they are. This is part of the reasons why star forts are developed.
You missed a few things... Living in a circular city, you have less travel time to get to more places. This means you can more easily defend the walls, and citizens can get to and from their houses, jobs, and/or markets faster, leading to a better defended, more prosperous city.
not to mention things like cities generally werent planned...
They happen naturally : P
azmanabdula that explains all the non-circular cities :P
Nemo's Channel USA we are looking at you!
:( you got us, most of our modern cities are generally in squares for simplicity of roadways, we really don't have to worry about defending our borders all that often anymore, just every once in a while
Andrew Having utilities in a grid format is so much easier...
Circles make everything so much more difficult...
As for defending your borders...
Isnt that what the Alamo was for?
Wink Wink
To protect the titans from Levi, duh..
Spoiler!!!
To protect the world from Eren
Curved walls are also stronger than sharply-angular ones.
and real men like curves
Why are they stronger? Against what kind of force/stress?
However using angles can create areas where you can strike the enemy from multiple sides.
@@olemew Round things stabilize themselves by their shape.
Eggs, for example. If you try to crush an egg with your fingers at the two ends furthest apart, you will find it very difficult. The pressure is distributed by the shape on the shell and it remains stable.
This also applies to other things with a round shape.
Other examples are balls, domes on buildings, or even walls to some extent.
@@eg-qv9ys Domes were used because they create open spaces and have religious symbolism, not because they were stronger against external forces. City-walls would never be crushed like an egg. Therefore, I still don't see how they are "stronger" or against any kind of stress (wind, catapults, etc.)
That first time playing AOE back in the day online...
You build a city in the middle and your team mate is like..
"Why!?"
To protect yourself from titans of course..
Seriously? xD
@@nosorryidontspeakoof278 omg I just replied to 3 year old comment aaa
It should be noted that your super round example in Germany is built in the impact crater of an ancient asteroid. They just built the wall according to the natutal terrain of the crater. BUT the asteroid and it's creater are both round because of the reasons you stated.
Thank you for the video.
0:30 - The case of Nördlingen is very special. It was built upon a meteorite crater.
The length of the arc is 74. 2 % the length of the median
The last tangle problem isn't correct... You pick random points on red line and blue line, how will you ensure that the circle passes through these random points? Also we need to make sure that the the circle cuts the triangle in equal areas... And what is the centre of that circle?
Excellent video
In the world I write about the people I write about most often either have circular or egg shaped cities.
For the same reason we have pyramids all around the world: feasibility
also the structure is stronger
very elegant
to keep the titans out of course ...(edit: lol i read the title as '''around'' instead of round, so jokes aside, pretty interesting video actually)
Nice vid!
Shiganshina
I didn't get the problem and its solution. If the curve we are looking for is a circular arc then the 2 starting points could not have been picked at random.
Think of all the curves connecting a red dot and a green dot. We only consider the curves that divide the area of the triangle in half. The question: which of these curves is the shortest. It ends up that the circular arc is the shortest.
Yes, but only if I have picked the 2 dots to be in specific places on the edges. If I have picked the 2 dots near the point that the red edge and the green edge intersect then the circular arc does not divide the triangle area in half. In this case another curve has to be picked as the shortest which do divide the area in half.
The argument in the video works no matter which green point and red point you choose. Remember, though, that the curve has to cut the area of the triangle in half. Even if the two points are close, you can always construct a curve that bisects the area.
+Tipping Point Math I have to say I'm confused about that part as well. When you change the blue shape to a circle, the green dots you chose earlier change position. Is that because that's just what we're trying to find here? The two points that give us the shortest possible curve that cuts the triangle in half?
Yes, we are trying to *show* that the appropriate sized circle is the shortest path that connects the green edge to the red edge while cutting the triangle into two equal-area regions. We are not assuming that the red and green points are fixed.
To protect humanity from man eating naked giants
Man-eating naked giants seems familiar to me.....
@@izumithegreat4597 Ahahaha nice one Freedom boy
Same reason bubbles are round. Highest capacity, Least materials.
Same reason grapes are most popular for making wine. Greatest volume of juice to surface area.
Great video!
Question: Why are walled cities round?
Me: To keep the titans out!!!! XD
Shinzou sasageyo
What about Vauban fortress, who became the standards later on
0:27 its tallinn not tallin
Trump joke at the beginning, lol.
?
lol😂😂
+
Not everything related to walls is related to Trump
didnt get the trick at 3:00
+Khalid M. Adel i just dont get it
what happens when i choose two dots near to the intersection of red and green it would then make a tiny circle and how is its area 50% of the whole thing
Circular walls are not good for defence actually.
Why not?
Because you need "jagged" walls and towers so that there are no blind spots for defenders.
Imagine attackers walk up to a circular wall. The only danger they can expect is from directly above their heads. If the wall doesn't have hoarding or whatever it's called, they are completely safe and can start digging under the wall.
Other examples in this video aren't bad, but that Nordlingen city doesn't even have proper towers. But they probably had some other reason to build it that way.
That's not entirely true and focuses on a very specific scenario.
idk y but, you missed CONSTANTINOPLE
Wtf is Carcassone?
Very good videp
xian is so rectangle.
Just a little confused here. A square doesn't have concave elements so how is a circle better than a square?
If a circle and a square have the same area, the circle's perimeter is shorter.
Not all walled cities are round, Tokyo (called Edo in the past) is spiral!
00:25 GoT?
That’s the filming location for kings landing, also many other filming locations are in different parts in Croatia, I live in Northern Ireland where the most filming took place which is pretty cool. 😎👌💯
like Baghdad
yay Uzbekistan is known
Walled cities are round because they listened to the Wooly Bully and decided not to be L7.
Yeah, I just did calculus and then felt stupid
I soooooooo perimetric!
thought you dropped off the face of the Earth
Alive and well. I'm building a team to help increase the rate of video production. Thanks for your support!
+Tipping Point Math That's great news! I love your vids! 👍
why not a triangle
It's quite simple to imagine volumetric structures of strong triangular form for practical purposes that are already exist such as roofs, tents, bridges , communication towers, geodomes, etc. The main aspects of reasoning would be: biological (sharp edges are unsafe/inconvenient, strict angles are alarming/threatening) and physical (overcomplicated building with optimal-sized instruments and resources is expensive). Otherwise, it is more appropriate to study superiority of triangular shapes in dynamic mechanisms or systems to increase theirs efficiency (e.g. reuleaux triangle, ternary computer, triangular screw). Also, triangular furniture and clothing are rather beautiful...
@@alexb3468 img.itinari.com/pages/images/original/ca3645ea-142b-4189-b9c2-29c408d82eb3-slide1.jpg?ch=DPR&w=1200&s=9174ba55770e999d9614dff2feb29aa4
Do some actual research please. A semi circle is as big as a full circle of the same parameter. The reason is the present of the coast. Also a curve through six points is generally not a circle. It's only a circle if both your starting and finishing point are mid points. Look at the change from the raw blue region to the circle, the points are moved. Busted.
Also, my guess is the curve with least eccentricity because a circular arc does not always bisect the triangle.
+Xuan Bach Lai you can actually choose two points so that when you replicate the triangle you get a circumference with radius R which bisects the resulting hexagon area
+Xuan Bach Lai and how is a semicircle as big as a full circle?
Perimeter_Area for each shape:
2PiR _ PiR^2 for the full circle
(Pi+2)r _ Pi(r/2)^2=Pi(r^2)/4 (i) for the semicircle
Equal perimeters:
2PiR=(Pi+2)r => R=r*[(Pi+2)/(2Pi)]
Substituting R in the full circle area:
Pi(r^2)*[(Pi+2)^2]/(4Pi^2)= [Pi(r^2)/4]*[(Pi+2)^2]/(Pi^2) (ii)
Dividing i and ii by Pi(r^2)/4 and comparing both:
1< [(Pi+2)^2]/(Pi^2)
So the full circle is bigger even if it has the same perimeter. Trivial.
Looks like TH-cam messed up my asterisks but you *should* be able to figure it out.
Ok, my bad on the semi-circle one. I messed up.
But about the bisecting thing, what I meant was that 2 random points on an 60 degree angle and a circular arc, copied 6 times, would not make a full circle. And no, there are cases when no circumference can satisfy because it would not fit into the triangle.
Just in the early ages of fortified cities you can find a circular shape of walls. Most common shape in medieval and renaissance walls is the star. A star shape is the opposite of your theory, and its the quintessential defensive structure shape in those ages.
the walls are not like a rope that you have to stretch to find the better shape, you literally build it in the shape you need to surround your city or the shape that give you advantages on defence during sieges. The only advantage in round shape is a lower use of materials needed to go around the city, but if a city is rich and has no lack of stone the engineers will chose a star shape, because when you build a fortification the only important thing is the defense strenght, and a round shape is probably the worst kind of fortification.
@@moderntube1 Hi, can you cite some examples of medieval big cities that are star shaped?
@@olemew Catania (Italy), Lucca (Italy), Elvas (Portugal), Palmanova (Italy), Naarden (Holland), Alba Julia (Romania)
en.wikipedia.org/wiki/Bastion_fort this is the wikipedia page aobut the italian fortification ("Fortificazione alla Moderna" in Italy) it says the complete opposite of this video about the shape of ancient walls.
@@moderntube1 Amazing! Thank you very much
AGAIN, STAY TUNED FOR MORE VIDS BY CAPTAIN OBVIOUS INCLUDING: 1) Why water runs downhill. 2) Why wood comes from trees. 3) Why eating makes you poop 4) where babies come from. 5) Why dogs don't meow 6) Why basements are not attics. 7) Why the rain doesn't fall up. 8) Why it gets dark at night ...and MUCH MUCH MORE!
first
WHY ARE WALLED CITIES ROUND? REALLY? That's a subject? First, that's a falsehood being that it's not near 100% true. (Google town walls / Images) So WITHOUT watching the vid, let me save you the trouble. The first building goes up in a most desirable location; everyone likes desirable locations, so they become neighbors on the next-to-most-desirable land. Tradingpost, church, bar and townhall follow near center and now you're on your way to City-hood. Now, since it's true, most towns spider web in all directions once established, yeah round, which is priority for protecting, THUS the wall's dimensions. NO MATH INVOLVED that's tougher than 1+1, folks ...Maybe you should produce a Vid on why holes get bigger when you keep digging in the same space. ...or maybe a Vid on why the simplistic gravitate toward TH-cam to simulate creativity with the most obvious of content. ...NEXT.
watch the video
+Don White
wow I wish we could be friends in real life, I'm sure you'd be great fun at a party, you don't sound like a jerk at all
Oh, come on. Can't ya take a joke? Actually, I'm just sticking around because I'm waiting for the follow-up, "Why tall buildings are called sky-scrapers". the suspense is killing me. -DW
@@A1Authority your joke sucks tho
@@mion1944 It's not about the stupid joke.. it's about the stupidity of the stupid video, Stupid.