subt More than 2,200 years ago,
a guy measured… …circumference of Earth
using a woodstick…

…and a camel.

you’re watching “La preuve par vieux”.

Hi. 2,200 years ago,
about two centuries… …before Cleopatra and Caesar;
it’s still the time of the egyptians…

…even though this time’s almost up…

…i mean, the great Egypt history’s time :
pharaohs and stuff… At this time stands
the Library of Alexandria… …one of the wonders of the world,
housing almost every existing documents… …philosophy, poetry,
mathematics, and so on. …and keeping and managing this library,
is a guy called Eratosthenes. Eratosthenes is a really, really,
i mean real-freakin-ly…

…smart.

We’ll talk about it.

2,200 years ago, it’s been a while since
first men hypothesized…

…that Earth was round.

But no one knows !

Many people think so,
but no one knows. Plato wrote about it,
about the Earth being round, which, of course, was then
obviously repeated by Aristotle, who even calculated
the circumference of the Earth…

Aristotle (sigh)

Aristotle calculated the circumference
of the Earth and estimated it was about…

400,000 stadia(=stadiums).

Stadium is the length — obviously,
at this time, they knew not about the metric system… …when they were measuring things.
They had goofy measurements… …such as pedes (feet), cubits, and so on,
that rely on the size…

…of the guy measuring…

…and they had some measurements
that were fixed… …as, for instacne, the stadium,
which is the length of Olympia’s Stadium.

that’s roughly about 160m (175yd).

So, he found out that Earth was
about 60,000km (37,280 mi)…

So, he was off…

…well, incredibly off !
Aristotle, huh… And please, do not explain
how you came up with that number…

…he went like that…

“400,000 stadia !”

“400,000 stadia, and heavy objects
fall fast !”

well : Aristotle !

Eratosthenes decides he will measure
the circumference of the Earth.

Why does he do that ?

Eratosthenes, at some point,
lives in Syena — former Aswan… That was before he went to live in
Alexandria — former…Alexandria

He had noticed something…

…on summer solstice, when the
Sun gets as high in the sky as possible…

…in Syena…

…when, in face, the Sun
got as high as it gets… …that high in the sky,
right before it starts going down…

…there’s a well, in Syena…

…and if you look into the well,
at this exact moment…

…the Sun doesn’t cast any shadow at all inside.

Eratosthenes, who knows his geometry 101,
infers quite simply… …that this is because the Sun is
exactly and vertically above the well. And this is when he has an idea,
a real bad*ss idea !

He asks a friend of his…

— whose name i don’t recall,
but seriously couldn’t care less —

…who lives in Alexandria…

…to wait for the summer solstice…

…when the Sun is getting high in the sky…

— so roughly at the same time
that it is over the well in Syena —

…to plant a gnomon in the ground…

— a gnomon is a stick, straight,
made of wood — — a feature of the gnomon is
that its length is stated — So he asks his friend to plant
a gnomon in the ground… …straight up,
as vertically as possible…

…and tells his pal :

“when the Sun reaches its highest point…”

“…you will measure the length
of the gnomon shadow on the ground.”

that dude…

that dude’s just awesome…

You’ll see that, from that,
this dude will measure…

the circumference of the Earth.

Quick note : it involves a few
geometry principle, nothing fancy, don’t worry,
we’ll go through that. The name’s more complex than
the principle itself…

— we’re quite accustomed to it —

it’s called : alternate interior angles.

Out loud, it may sound terrible,
but when you draw it, it’s obvious…

Two parallel lines…

…and a third line that cut through
those parallel lines…

…and you get, well, angles (duh).

Well, between those parallel lines (“interior”),

on each side of the third line
(“alternate”),

angles are equal.

At this point he has another idea…

— really, the most brilliant idea
Erastosthenes had about this — …to consider the fact that the Sun is
so far from us…

…that we can say its rays are parallel.

If this is not a damn-that’s-epic idea,
i don’t know what it is. Guys do not even know whether
the Earth is round…

It’s merely a hypothesis !!

And so, at the proper time,
when the Sun casts no shadow…

…over the well in Syena…

…but casts a shadow over
the gnomon in Alexandria… …rays of the Sun over both places
are perfectly parallel. What’s the difference ? The ray
hitting the well in Syena…

…since it’s vertical…

…heads straight towards
the center of the Earth…

– if the Earth is round…remember –

On the other side,
the ray hitting the gnomon… …is not heading towards
the center of the Earth… …but the gnomon,
being vertically planted… …is heading towards
the center of the Earth. – once again…
if the Earth is round – So you see, on the drawing,
that you can easily spot…

…the two rays as the parallel lines,

…and the third line, which
extends the gnomon…

…towards the center of the Earth.

Hence, if you can measure the angle
formed by the gnomon and its shadow,

It’s exactly the same angle…

…as the one formed by
Syena and Alexandria…

…with the center of the Earth.

So he gets to his pal and tells him
“gimme your numbers”.

From those measurements, he then draws…

…the gnomon and the shadow,
and calculates the angle.

He then wonders :

“How many time can i repeat this angle…”

“…to get a full turn?”

the angle was 7.2°.
Obviously, they weren’t calculating with degrees… but all right…i give you this one.
Spoiler alert : it was 7.2° So the answer to the question “how many
times do i repeat the angle” “to get a full turn?”
the answer was 50 times. Now he says :
“Ok, so if i measure the distance…”

“…between Syena and Alexandria..”

“…and repeat this distance 50 times…”

“…i will have measured the girth of the planet.”

And that’s exactly what he’s going to do…

Except…

…Syena to Alexandria…

…is a long walk.

So he’s going to get himself
the services of, i’d say,

one of the most incredible jobs at that time.

A bematist.

So : what is a bematist ?

– had i lived then, 2,200 years ago,
i would’ve been a bematist…

…those guys rock !

A bematist is a guy
who measures long distances… …counting the steps of his camel
as he’s riding through the distance.

Camel step is supposed to be quite regular…

…so if you know its length (the bémâ)…

…and if you count the camel steps…

…you can infer the total distance.

I really don’t know what to say
(really, i mean : what?)

…they’re going to calculate the distance…

…between Syena and Alexandria…

…counting the steps of a freaking camel !

And they will get incredibly close to accurate measurement

— Whereas Aristotle is way over his head —

So, they ask a bematist to calculate the distance…

…and the bematist comes up with :
5,000 stadia. 5,000 stadia, that’s a little less than
800 km (around 500 mi).

5,000 stadia !

Eratosthenes now repeats 50 times this result…

…and finds out that the circumference of the Earth…

…is 250,500 stadia.

250,500 stadia, that’s about
39,500 km (24,550 mi).

What you need to know is that…

…the line from Syena to Alexandria
is almost a South-North line…

So he didn’t measure a longitudinal circumference…

…but the girth that goes through
North and South poles… With nowadays technology,
laser, satellites, and so on…

…we now know that this exact distance is in fact…

40,003 km (24,856 mi).

He was off 503 km (306 mi) on the total measurement.

2,200 years ago !

One may think whatever about Aristotle,

i hold no grudge against Aristotle…

— as far as i’m concern, there’s really no need…

Eratosthenes, what he did…

…if it isn’t an exact…

…definition…

…of a genius…

— that guy calculated the girth of our planet…

— with incredible accuracy…

— only assuming it was round !

He never said :
“Here’s the circumference of the Earth !” He sais :
“i don’t know whether the Earth if round or not…”

“…but if it is…”

“…here’s its circumference !”

One thing’s for sure

Eratosthenes has really been up

…to being a story of “La preuve pas vieux”.


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