Pi (1998)

PI
movie 1998

http://www.imdb.com/title/tt0138704/



One: Mathematics is the language of nature.
Two: Everything around us can be represented and understood through numbers.
Three: If you graph the number of any system, patters emerge.


You fly to high,
you'll get burnt.


Have you met Archimedes?
You remember Archimedes of Syracuse? Eh?
The king asks Archimedes to determine if a present
he has received is actually solid gold.
Unsolved problem at the time.
It tortures the great Greek mathematician for weeks.
Insomnia haunts him and he twists and turns in his bed
for nigs on end.
Finally, his equally exhausted wife,
forced to share a bed with this genius,
convinces him to take a bath, to relax.
While he's entering the tub,
he notices the bath water rise.
Displacement - a way to determine volume,
and thus a way to determine density.
Weight over volume.
And thus Archimedes solves the problem.
He screams, "Eureka!"
and he is so overwhelmed,
he runs naked through the streets to the king's palace
to report his discovery.

Now, what is the moral of the story?
- That a breakthrough will come.
Wrong! The point of the story is the wife.
You listen to your wife, and she'll give you persepective.
Meaning, you need a brak.



I'm not interested in your money.
I looking forward to understand our world.

I don't deal with materialist like you.



Remember Pythagoras.
Mathematician, cult leader.
Athens, circa 500 BCE.
Major belief: The universe is made of numbers.
Major contribution: The golden ratio.
Best represented geometrically as the golden rectangle.
Visually, there exists a graceful equilibrium
between its length and width.
When it's squared, it leaves a smaller golden rectangle behind,
with the same unique ratio.
The squaring can continue smaller and smaller,
to infinity.

Remember da Vinci.
Artist, inventor, sculptor, naturalist.
Italy, 15th Century.
Rediscovered the balance perfection of the golden rectangle
and penciled it into his masterpieces.
Connecting a curve through the concentric golden rectangles.
You generate the mythical golden spiral.

Pythogoras loved this shape,
for he found it everywhere in nature -
a nautilus shell, rams' horns, whirlpools, tornadoes,
our fingerprints, our DNA and even our Milky Way.
...
My new hypothesis:
If we're built from spirals,
while living in a giant spiral,
then everything we put our hands to is infused with the spiral.

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Story of Maths:2-The Genius of the East

THE STORY OF MATHS
Part.2
THE GENIUS OF THE EAST

http://www.open2.net/storyofmaths/
http://en.wikipedia.org/wiki/The_Story_of_Maths

http://stagevu.com/video/kxgbdlgmlvlh
http://www.imdb.com/title/tt1926910/


EXCERPTS:


THE GENIUS OF THE EAST

[China, India, Muslim, Italy]


CHINA
Chinese used Decimal Place Value system.
units, tens, hundreds, thousands ...

Ancient Chinese didn't have a concept of Zero.
It didn't exist as a number.


Odd numbers are seen as male, even numbers as female.
The number 4 is to be avoided at all costs,
number 8 brings good fortune.


In 1809, while analyzing a rock called Pallas in the asteroid belt,
Carl Friedrich Gauss,
who would become known as the prince of mathematics,
rediscovered this method
which had been formulated in ancient China centuries earlier.
Once again, ancient China streets ahead of Europe.


By the 13th century,
Golden Age of Math in Chinese
Important mathematician: Qin Jiushao
He came up with squared and cubic equations/formulas

"What's striking is that Qin's method for solving equations
wasn't discovered in the West until the 17the century,
when Isaac Newton came up with a very similar approximation method."


INDIA
India used Decimal Value System
"It's been suggested that the indian's learned the system
from Chinese merchants travelling in India with their counting rods."

Indians refined and perfected it,
creating the ancestors for teh nine numerals used across the world today.

But there was one number missing.
and it was the INDIANS who would introduce it to the world.
The earliest known recording of this number dates from the 9th century,
though it was probably in practical use for centuries before.
ZERO.


Before the Indians invented it
There was no number zero.
To the ancient Greeks, it simply hadn't existed.
To the Egyptians, the Mesopotamian, and as we've seen, the Chinese,
zero had been in use but as a placeholder, an empty space
to show a zero inside a number.

The Indians transformed zero from a mere placehoder
into a number that made sense in its own right -
a number for calculation, for investigation.


NEGATIVE NUMBERS
"The Indians called them 'debts' because they solved equations like,
"if i have three batches of material and take four away,
haw many have i left?"
"

TRIGONOMETRY
"Although first developed by the ancient Greeks,
it was in the hands of the Indian mathematicians
that the subject truly flourished."


When the moon is half full,
 because that's when it's directly opposite the sun,
So the Sun, Moon and Earth create a right-angled triangle.
Now, the indian could measure
that the angle between the Sun and the observatory
was one-seventh (1/7) of a degree.
The Sine function of 1/7 of a degree gives me the ratio
of 400:1.
This means the sun is 400 times further from Earth than the moon is.

So using trigonometry,
the Indian mathematicians could explore the solar system
without ever having to leave the surface of the Earth.


Pi is the ratio of the circle's circumference to its diameter.
any measurements involving curves soon require pi.

It was in 6th century India that the
mathematician Aryabhata gave a very accurate approximation for pi
- namely 3.1416.

I was taught at university that this formula for pi
was discovered by the 17th-century German mathematician Leibniz,
but amazingly, it was actually discovered here in Kerala.
two centuries earliest by Madhava.


It seems incredible that the Indians made these discoveries
centuries before Western mathematicians.
And it says a lot about our attitude in the West to
non-Western cultures
that we nearly always claim their discoveries as our own.


As the West came into contact more and more with the East,
during the 18th and 19th centuries,
there was a widespread dismissal and denigration.
of the cultures they were colonizing.
The natives, it was assumed couldn't have anything
of intellectual worth to offer the West.
it's only now, at the beginning of the 21st century,
that history is being rewritten.


Muslims Maths
In the 7th century, a new empire began to spread
across the Middle East.
The teachings of the Prophet Mohammad inspired a vast
and powerful Islamic empire which soon stretch from India in the east
to here in Morocco in the West.


The Muslim scholars collected and translated many ancient texts
effectively saving them for posterity.
In fact, without their intervention, we may never have known
about the ancient cultures of Egypt, Babylon, Greece and India.

But the scholars at the House of Wisdom weren't content
simply with translating other people's mathematics.
They wanted to create a mathematics of their own,
to push the subject forward.


In fact, the need of Islam demanded mathematical skill,
The devout needed to calculate the time of prayer
and the direction of Mecca to pray towards.


Mohammad al-Khwarizimi

These numbers were now known Hindu-Arabic numerals
These numbers - one to nine and zero.
We use today all over the world.

But Al-Khwarizmi was to create a whole nw mathematical language.
ALGEBRA.
it was named after the title of his book al-Jabr w'al-Muqabala
or Calculation By Restoration Or Reduction.


Previously, the Indians and the Chinese
had considered very specific problems,
but al-Khwarizmi went from the specific to the general.


PERSIAN MATHEMATICIAN

OMAR KHAYAM
Poet = Mathematician , Rubaiyat
Cubic Equations.



ITALY

During the centuries in which China, India, and teh Islamic empire
had been in ascendant,
Europe had fallen under the shadow of the Dark Ages.

But by the 13th century, things were beginning to change.

Led by Italy, Europe was starting to explore and trade with East.
With that contact came the spread of Eastern knowledge to the West.

 
That mathematician was Leondardo of Pisa, better known as Fibonacci.
and in his Book of Calculating,
Fibonacci promoted the new number system (Hindu-Arabic numerals)
demonstrating how simple it was compared to the Roman numerals.


The city of Florence even banned them in 1299 (Hindu-Arabic numerals),
but over time, common sense prevailed,
the new system spread through Europe,
and the old Roman system slowly became defunct.



FIBONACCI NUMBER [1 1 2 3 5 8 13 21 34 55 ...]
The Fibnonacci numbers are nature's favorite numbers.
It's not just rabbits that use them.
You count the number of petals on a flowr is invariably a Fibonacci number.
You find these numbers running up and down pineapples if you count the segments.
Even snails use them to grow their shells.
Wherever you find growth in nature, you find the Fibonacci numbers.


Next breakthrough in Europe wouldn't happen until 16th century.


TARTAGLIA
Facial scar and stammerer
cubic equations

It was the first great mathematical breakthrough to happen in modern Europe.

It was time for the Western world
to start writing its own mathematical stories
in the language of East.

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