0:00:15.526,0:00:17.050
This image of the Vitruvian Man,

0:00:17.074,0:00:18.302
taken from Leonardo's sketches,

0:00:18.326,0:00:20.184
has become one of the most recognizable

0:00:20.208,0:00:21.625
symbols of the Renaissance.

0:00:21.649,0:00:22.719
But why?

0:00:22.743,0:00:24.696
It's a simple pen and ink drawing, right?

0:00:24.720,0:00:25.979
Wrong!

0:00:26.003,0:00:27.373
Let's start to answer this question

0:00:27.397,0:00:28.610
with a math problem.

0:00:28.634,0:00:30.777
I know how to calculate[br]the area of a circle.

0:00:30.801,0:00:32.075
I take the value for pi

0:00:32.099,0:00:34.323
and multiply it by the radius squared.

0:00:34.347,0:00:36.541
I also know how to take[br]the area of a square.

0:00:36.565,0:00:39.340
I multiply the base by itself.

0:00:39.364,0:00:41.384
But how can I take the area of a circle

0:00:41.408,0:00:43.775
and create a square with an equal area?

0:00:43.799,0:00:45.715
This is a problem often[br]called "squaring a circle"

0:00:45.739,0:00:48.023
that was first proposed[br]in the ancient world.

0:00:48.047,0:00:49.634
And like many of ideas[br]of the ancient world,

0:00:49.658,0:00:51.870
it was given new life[br]during the Renaissance.

0:00:51.894,0:00:53.054
As it turns out,

0:00:53.078,0:00:54.442
this problem is impossible to solve

0:00:54.466,0:00:56.066
because of the nature of pi,

0:00:56.090,0:00:57.888
but that's another story.

0:00:57.912,0:00:58.602
Leonardo's sketch,

0:00:58.626,0:00:59.856
which is influenced by the writings

0:00:59.880,0:01:01.881
of the Roman architect, Vitruvius,

0:01:01.905,0:01:03.486
places a man firmly at the center

0:01:03.510,0:01:05.483
of a circle and a square.

0:01:05.507,0:01:06.818
Vitruvius claimed the navel

0:01:06.842,0:01:08.079
is the center of the human body

0:01:08.103,0:01:09.605
and that if one takes a compass

0:01:09.629,0:01:11.534
and places the fixed point on the navel,

0:01:11.558,0:01:13.991
a circle can be drawn[br]perfectly around the body.

0:01:14.015,0:01:15.980
Additionally, Vitruvius recognized

0:01:16.004,0:01:17.082
that arm span and height

0:01:17.106,0:01:19.726
have a nearly perfect[br]correspondence in the human body,

0:01:19.750,0:01:22.833
thus placing the body perfectly[br]inside a square as well.

0:01:22.857,0:01:24.207
Leonardo used the ideas of Vitruvius

0:01:24.231,0:01:27.003
to solve the problem of squaring[br]a circle metaphorically

0:01:27.027,0:01:29.711
using mankind as the area for both shapes.

0:01:29.735,0:01:32.587
Leonardo wasn't just thinking[br]about Vitruvius, though.

0:01:32.611,0:01:33.791
There was an intellectual movement

0:01:33.815,0:01:34.889
in Italy at the time

0:01:34.913,0:01:36.297
called Neoplatonism.

0:01:36.321,0:01:37.717
This movement took an old concept

0:01:37.741,0:01:40.421
from the 4th century developed[br]by Plato and Aristotle,

0:01:40.445,0:01:42.254
called "The Great Chain of Being".

0:01:42.278,0:01:44.659
This belief holds[br]that the universe is a hierarchy

0:01:44.683,0:01:45.590
resembling a chain,

0:01:45.614,0:01:47.755
and that chain starts at the top with God,

0:01:47.779,0:01:49.712
then travels down through the angels,

0:01:49.736,0:01:50.289
planets,

0:01:50.313,0:01:50.878
stars,

0:01:50.902,0:01:51.958
and all lifeforms

0:01:51.982,0:01:54.042
before ending with demons and devils.

0:01:54.066,0:01:55.789
Early in this philosophic movement,

0:01:55.813,0:01:58.147
it was thought[br]that mankind's place in this chain

0:01:58.171,0:01:59.503
was exactly in the center.

0:01:59.527,0:02:01.202
Because humans have a mortal body

0:02:01.226,0:02:03.134
accompanied by an immortal soul,

0:02:03.158,0:02:05.284
we divide the universe nicely in half.

0:02:05.308,0:02:07.043
Around the time Leonardo sketched

0:02:07.067,0:02:08.662
the Vitruvian Man, however,

0:02:08.686,0:02:10.847
a Neoplatonist named Pico della Mirandola

0:02:10.871,0:02:12.212
had a different idea.

0:02:12.236,0:02:13.790
He pried mankind off the chain

0:02:13.814,0:02:15.957
and claimed that humans[br]have a unique ability

0:02:15.981,0:02:17.621
to take any position they want.

0:02:17.645,0:02:19.204
Pico claimed that God desired

0:02:19.228,0:02:20.752
a being capable of comprehending

0:02:20.776,0:02:23.545
the beautiful and complicated[br]universe he had created.

0:02:23.569,0:02:25.464
This led to the creation of mankind,

0:02:25.488,0:02:27.584
which he placed at the center[br]of the universe

0:02:27.608,0:02:30.018
with the ability to take[br]whatever form he pleases.

0:02:30.042,0:02:32.117
Mankind, according to Pico,

0:02:32.141,0:02:34.678
could crawl down the chain[br]and behave like an animal

0:02:34.702,0:02:36.899
or crawl up the chain[br]and behave like a god,

0:02:36.923,0:02:38.204
it's our choice.

0:02:38.228,0:02:39.457
Looking back at the sketch,

0:02:39.481,0:02:41.567
we can see that by changing[br]the position of the man,

0:02:41.591,0:02:43.306
he can fill the irreconcilable areas

0:02:43.330,0:02:44.986
of a circle and a square.

0:02:45.010,0:02:47.289
If geometry is the language[br]the universe is written in,

0:02:47.313,0:02:48.694
then this sketch seems to say

0:02:48.718,0:02:50.493
we can exist within all its elements.

0:02:50.517,0:02:52.034
Mankind can fill whatever shape

0:02:52.058,0:02:53.329
he pleases geometrically

0:02:53.353,0:02:55.248
and philosophically as well.

0:02:55.272,0:02:56.328
In this one sketch,

0:02:56.352,0:02:57.618
Leondardo was able to combine

0:02:57.642,0:02:58.424
the mathematics,

0:02:58.448,0:02:59.106
religion,

0:02:59.130,0:02:59.920
philosophy,

0:02:59.944,0:03:00.780
architecture,

0:03:00.804,0:03:02.503
and artistic skill of his age.

0:03:02.527,0:03:04.242
No wonder it has become such an icon

0:03:04.266,0:03:06.278
for the entire time period.