This video was made possible by Brilliant. Learn with Brilliant for 20% off by being

one of the first 200 to sign up at Brilliant.org/HAI. You know what would make a bad video? One on, “what’s the longest border in

the world,” because it’s this one—the US-Canada border. Done. You know what would make a slightly less bad

video? One on “what’s the shortest border in

the world” since the answer’s a bit more complicated. Alright let’s beat that bush… or around

it or something. There are plenty of small countries with short

borders such as Monaco which shares a 2.7 mile, 4.4 kilometer long border with France

and the Vatican which shares 2 mile, 3.2 kilometer border with Italy but there are bigger countries

that share shorter borders such as the UK and Spain. Of course the British Isles are nowhere near

Spain but the British territory on the Iberian Peninsula is. Despite how it may look I’m not talking

about Malaga, I’m talking about Gibraltar. This British overseas territory shares a 0.8

mile, 1.2 kilometer border with Spain which is not the shortest international border in

the world. Down in Africa, there exists a pretty unique

border where Botswana, Zimbabwe, Zambia, and Namibia come close to forming the only place

on earth where four countries meet at one point. In the past it was thought that this was maybe

a quadripoint but nobody was really sure. Many of the post-colonial era borders were

not super well defined. Right here, at this point, Namibia, which

was controlled by South Africa at the time, said that the border was a quadripoint with

four countries meeting at one point while Botswana said that the border looked like

this with them having a tiny little border in the Zambezi River with Zambia which was

important to them since there was a ferry across the river which served as the only

direct connection between the two countries. If the border did indeed look like this as

South Africa said it did, every ferry trip would illegally be entering into their territory. So, South Africa/Namibia shot some guns and

everyone lived unhappily ever after, until around 2007 when the four countries sat down,

did some diplomacy, and decided that Botswana did indeed share this tiny, 500 foot, 150

meter border with Zambia which made everyone happy, except for this guy. What’s more, they decided to build a bridge

to link the two countries which will be done in 2019 and will take this big old curve in

order to very decisively stay out of Namibia and Zimbabwe’s territory. Now, this tiny border does qualify as the

shortest overall border between two countries, as in, the total border distance two countries

share, but as I’m sure you can tell by us being only halfway through this video, there

are shorter single portions of borders between two countries. Exclaves, territories of a country surrounded

by that of another, are the key to shorter border portions. You can look at a place like Baarle-Nassau. The easiest way to describe this town is like

this—this is Belgium, this is the Netherlands. It’s just a messy puzzle of exclaves the

smallest of which is this one. This strange Belgian portion of an empty field

has a border length of 800 feet or 250 meters making it a very short border, but still longer

than that Botswana-Zambia border. But, remember that time back at the end of

the 19th century when Europe decided it’d be cool to just take all of Africa? Then, do you remember that time 50 years later

when Europe decided it’d be cool to just leave all of Africa? See, look Spain is doing a great job at leaving. Nice job Spain! There you go! Almost done! Oh wait, Spain, you forgot a bit. Spain? Spain what about these bits? Spain? Half a century later, in two-thousand-now

Spain still holds these territories in Africa. Ceuta and Melilla are fairly well known as

they’re decently sized cities but there are more Spanish territories in North Africa. Six islands just off the coast of Morocco

are controlled by Spain. It’s worth noting, all of the Spanish Territories

in North Africa are disputed territory with Morocco but each of them is controlled by

Spain. In addition to those six islands Spain has

another bit of territory in mainland Africa—Peñón de Vélez de la Gomera. This tiny rock was once an island but a huge

storm in the 30s formed this thin strip of sand that connected it with mainland Africa. The Spanish territory is only inhabited by

a few dozen Spanish soldiers who’s whole purpose is to sit around and make sure the

Moroccans don’t take it. It’s not that this peninsula is strategically

important at all anymore—it’s just that the Spanish believe that giving this territory

to Morocco would open the political floodgates for them returning Ceuta and Melilla to Morocco. The Spanish soldiers can’t cross into Morocco

and Moroccans can’t cross into this bit of Spain so all supplies and personnel are

flown in by helicopter to this heliport. Because this was formally an island, the border

just spans over the sand strip which makes it exceptionally short. The distance from here to here is just 278

feet or 85 meters and this is therefore, almost certainly, the shortest international border

in the world. You probably don’t need an advanced understanding

of geometry to figure out how long this border is but you probably do to answer this: how

many times greater is the green area than the blue area in this image? If you think you know the answer leave it

in a comment but if you don’t, you should take Brilliant’s geometry course. It teaches you the intuitive concepts behind

geometry so you don’t just learn how to answer questions, you understand it. If geometry isn’t your thing, Brilliant

also has tons of superbly designed courses on topics like logic, statistics, waves and

light, and more. To learn more about Brilliant, go to https://brilliant.org/HAI/

and sign up for free, and also, the first 200 people that go to that link will get 20%

off the annual Premium subscription.

Ooo boy, 1k more subs and you hit the 1 mil milestone

04:29 answer is 9r^2

4:29 im not totally sure but i would say 9(i did not pull that up my butt)

explanation:

i claimed small half circle diameter as 2 and the big green one had a diameter of 6

i assumed pi as 3 and that meant 2.2.3 equals 12 and 6.6.3 equals 108.

the green ones land was 9 times greater than the blue

Who's watching after 1mil?

That area is 1/3 times that of the larger area.

G = (B * 3)

The green part is 62,5% larger than the blue one

2 or 3 times

3x bigger

The answer is three!!!

4:31 the answer is 2 times

SPAINGreen is 5 times greater

Ceuta y Melilla son españolas desde mucho antes de que existiera Marruecos, son ciudades españolas, no son colonias.

0:21 aaand good for watchtime?

Geometry puzzle: 3 times bigger.

We are including 2 or more countries, so there is a shorter border you shit-stained distilled water bottle, and it is Slovenia-Austria-Italy border, it is a fucking point.

s p a i n

I live in morroco my boy

The green area is nine times bigger

Two thousand and now

The blue area has the same circumference as the green are because the green is 3x the length of 1 blue

3 x pi ÷ 2 + 3 = 7.71 rounded

1 x pi ÷ 2 + 1 x 3 (cuz there are 3) = 7.71 which is the same

7.71 = 7.71 = 1:1 ratio

1m SUBS!!!!

Problem at the end: The green area is twice the blue area.

Breakdown below the cutoff…

Definitions:

A = green area

a = blue area

R = large radius

r = small radius

R = 3r

a = 3 half blue circle with radius r

a = 3 × [(π r^(2))/2] = [3πr^(2)]/2

A = 1 half circle with radius R minus blue area 'a'

A = [πR^(2)]/2 – [3πr^(2)]/2

= (π/2)[R^(2) – 3r^(2)]

= (π/2)[(3r)^(2) – 3r^(2)]

= (π/2)[9r^(2) – 3r^(2)]

= [6πr^(2)]/2

= 3πr^(2) = A

2a = A

Therefore, green is twice the area of blue.

Green is 2 times as big

1:55 Read the fine print in the bottom right corner…

4:27 its 5 times greater?

We need dimensions to answer the question

The green semicircle is 6 times larger than the 3 blue semicircles

9

1,5 timez

Englands one of the biggest country in the biggest countrys in the world as we own the falklands.

Argentines:

angry hitler noises4:32 answer:11

3 times

whips out a notepad and a pencilThe green shaded area is 2 times bigger than the blue shaded area69

It's three times bigger.

Base unit: x

Green area: pi*(x/2)^2

Blue area: 3*pi*(x/6)^2

Ratio: (Green area/Blue area) = [pi*(x/2)^2]/[3*pi*(x/6)^2] = [(x/2)^2]/[3*(x/6)^2] = (1/3)*[1/4]/[1/36] = (1/3)*(36/4) = 3

If I would do it again, I would use 6x as a base unit so as not to have to deal with fractions because; nobody likes fraction.

(Or use integrals because it's more fun than geometry)

Green is twice as big

those are enclaves not exclaves 2:32

What if there was a border that was one nanometer

The green area is twice as large as the blue

Let's assume that the diameter of 3x. Then the green plus blue is (3x)^2 times π, aka π(9x^2nd). The diameter of the blue half circles is x, because each makes up 1/3 of the previous diameter, so each individual circle is πx^2nd. Since there's three, the total blue area is π(3x^2nd). The total area minus the blue equals the green, so the green area is π(6x^2nd). That is two times larger than π(3x^2nd), so the green is two times larger than the blue.

Is the bridge done yet?

The green area is twice as large as the blue area.

1:55 Here's the review: https://goo.gl/maps/KY6nhW3edQQgK1oK6

SPAIN???for the brilliant.org question at the end;

gc=green circle

bc=blue circles

gsc= green semi-circle

bsc=blue semi-clircle ;

first, let's calculate the areas of each of the following objects,

one bc radius is 1; so

gc=pi*3^2=

pi*9=

28.274

bc=pi*1^2=

pi*1=

3.14

gsc=gc/2=

14.137

bsc=bc/2=

1.57

then, we ask the question;

"How many times bigger is gsc then bsc?"

let x equal how many times bigger gsc is than the bcs total area,

x=gcs/(bcs*3)

x=14.137/(1.57*3)

x=14.137/4.71

x=~3

the green area is roughly 3 times bigger than the blue area.

Is the narrator trying to make me feel bad for the accomplishments of the Western world and colonialism? Some serious guilt from him hahah

That was almost a terrible, unnecessary, and offensively unintelligent video, but managed to be just ok.

Found the review.

https://goo.gl/maps/s4b8zg5PxdJvkj729

spain

https://goo.gl/maps/iLTJD9K1rseVDCwV7

Ceuta has been spanish since the 1500s and it was previously owned by the Portuguese. Similar story with Melilla. It has little to do with ninteenth century colonialism.

Half circles are equal size…

Ok, we're going to get extremely pedantic here. The question asked "How many times greater is the green area than the blue area?"

Now, that sounds simple enough, and the math is indeed simple. The phrasing and the exact meaning of the phrasing of the question make it a bit more interesting.

First, the math. This is easy the green area is 2 times the size of the blue area. I'm not going to explain the math because that's easy and it's not my point. The more interesting thing is the phrasing of the question. How many times greater is the green area than the blue area? Let's say that blue had an area of 1. Then we know that green has an area of 2. How many times greater is 2 than 1? It's important to know that asking how much bigger is not the same as asking how many times as big. 2 is 2 times as big as 1. That is, 2 is 200% of 1. But how many percent bigger than 1 is 2? To find percent change you take the new value (2) minus the old value, (1) and divide by the old value (1). That's (2-1)/1. The answer is 1.

So, how many times greater is the green area than the blue area?

1.

I know everyone will argue with me, but given the phrasing of the question, that is actually the correct answer.

4:32 I think it's 3 times greater

Haha, look at Spain, those colonial morons. Still hanging on to a fucking band-aid strip of land, because humans are fucking worthless monkeys.

The green area is 3 times as big as the blue area

There are 2 small islands in Lake Ontario that has a 32 feet Canada USA border https://www.atlasobscura.com/places/zavikon-island

Green area has twice the area the blue area does. To calculate the area of a semi circle you need to multiply pi by the radius squared by 0.5. So basically if you have 3 times the radius, since the difference is exponential, each blue semi circle can fit 9 times in the big semi circle. You have 3 small ones, and 9 – 3 is 6, and 6 is 2 times 3, the green area is twice as large as the blue one.

Green Area = 3 x Blue Area

A = (pi)×R^2 & R = d/2

Blue Area = 3*(pi)(d/2)^2 = 3(pi)*(d^2)/4

Green Area = (pi)×(D/2)^2

D = 3d

Green Area = (pi)×(3d)^2/4 = 9(pi)×(d^2)/4 = 3 × Blue Area

Arrrrrrgggghhhh….I forgot to cut my areas in half….Math classes were a LOOOONG time ago.

3

I know this answer!

Jesus Christ that Google review

There's a quadpoint where Mongolia, Kazakstan, China and Russia meet.

Green is 3x larger than blue

It’s an optic level illusion and the green area is the same as the blue area

Spain

GIBRALTAR

It’s four times bigger boi

Spain…….

During high tides the border even become more short

This video was not that short

The answer to the Brilliant question is the green area is twice the size of the blue area.

ASSUME:

*The figure is an exact semicircle

*The blue area is made up of three congruent semicircles

PROOF:

-Declare the radius of each blue semicircle to be x

-The area of each blue semicircle is (πx^2)/2

-The blue area is (3πx^2)/2

-The radius of the large semicircle is 3x

-The area of the large semicircle is [π(3x)^2]/2 = (9πx^2)/2

-The green area is the large semicircle less the blue area, (9πx^2)/2 – (3πx^2)/2 = (6πx^2)/2

-The scale factor of the areas is (6πx^2)/2 ÷ (3πx^2)/2 = 2

.•. The green area is twice the size of the blue area

i dont see anyone else commenting on the bomb ass music, and what song it is. i've looked on epidemic but idk which category it's under lmao

6

A corolla is 4,5 meters, the border is 85 meters, 10 corollas: 45 meters. 20 corollas: 90 meters. You can fit roughly 18 to 19 corollas in the smol border.

Ayyyyy lets go!!!

3 times as big

Green is 8 times bigger

4:26

Shouting in the backgroundIts 3!S p a I n

What about the Dutch, Belgian and German border in Vaals?

4:26 The green suraface is 2 times greater than the blue one

Isn't there a quadpoint in the sputh of Marokko with Algeria and two other countries that i don't know the name of😅

You forgot the little Spanish island called Perejil Island which is the Strait of Gibraltar near the coast of Morocco. Cool video.

I found the link to the bad review… I paused the video at the that point and saw the caption in the bottom right hand corner, read it, looked for the location on Google Maps, found out it was called the Kazungula Ferry, looked that up, found the lowest reviews through the filter, strolled down a bit, and found the review. Here: https://www.google.com/search?source=hp&ei=tXloXaGxL6ip_QaY0Z7gBA&q=Kazugula+Ferry&oq=Kazugula+Ferry&gs_l=psy-ab.3..0i13l5j0i22i30l5.3828.11060..11398…0.0..0.105.1091.11j2……0….1..gws-wiz…….35i39j0j0i131j0i67j0i10j0i13i30.Vo1_KtaOgcg&ved=0ahUKEwjh35fZtqnkAhWoVN8KHZioB0wQ4dUDCAc&uact=5#lrd=0x195a9f972b0c1b3b:0x3ce8df52a5e6486d,1,,,

What about emabasseys they must have they shortest borders

Green is twice as big than blue area, 9/2pi(x2) to 3/2pi(x2) if x is the radius of the blue semicircle, so green is 6pi(x2)

1/3

Blue Areas are 3 times smaller than green Area

1 star not enough countries touching

9

Exactly twice as big

4:30 it’s 3 times as big

whats the middlest

https://www.google.com/maps/place/Kazungula+Ferry/@-17.7902545,25.2636301,17z/data=!4m17!1m9!3m8!1s0x1f2cb893f9e934c9:0x38bcab1649b19452!2sZambezi+River!3b1!8m2!3d-14.9818834!4d29.5237367!9m1!1b1!3m6!1s0x195a9f972b0c1b3b:0x3ce8df52a5e6486d!8m2!3d-17.7902596!4d25.2658188!9m1!1b1

i found it i dont get anything

4:30

1.39 times bigger?

Whats the shortest border?

My 1mm Toy.

Lol that Google reviewer needs to get a life

1:55 https://goo.gl/maps/eKx7f4ziA1WN3La68