Beauty of Mathematics

This is a beautiful video! Watch this!
http://www.youtube.com/watch?v=h60r2HPsiuM

It is fascinating to see how most mathematicians describe mathematics as beautiful and aesthetic creative art. They often compare mathematics with music and poetry...

Math Videos

http://www.youtube.com/watch?v=imAh-lQsNJM&feature=related
http://www.youtube.com/watch?v=D1WQvIvdZS4
http://www.youtube.com/watch?v=dD65vFLnW1c
http://www.youtube.com/watch?v=7VCYgCNOuEM

How big is the million?

What do you think, how big is the million?

Let's try to count together...

Mathematics and philosophy: the most powerful combination

Have you ever thought why all famous mathematicians were also great philisophers?

The history of "0"

Many years ago there was no zero. Also, though people  knew the concept nothing, there was no mathematical notation for it.

Graphs

This is a fun video explaining the graphs:

http://www.youtube.com/watch?v=-cSm_D7MrRI
Here is another link with a lesson on graphs:
http://www.youtube.com/watch?NR=1&v=W9BhzvLooI4&feature=endscreen

Pascal and gambling

As I already mentioned, Pascal is famous for his contributions to probability. He took a strong interest in gambling, and developed a fundamental theory used by professional poker players today. In addition to professional gamblers, many economists gained valuable information from Pascal, particularly actuarial scientists.

Pascal's Triangle

Despite his accomplishments in all other spheres, Pascal was first of all a great mathematician. He helped to create two major new areas of research: projective geometry and probability theory, which has become important in such fields as actuarial, mathematical, and social statistics and as a fundamental element in the calculations of modern theoretical physics.
For many people, Pascal’s name is most recognized with its connection to Pascal's Triangle. Although he was not the first to study the Pascal triangle, his work was the most important on this topic. Pascal’s triangle has many mathematical associations, but Pascal discovered its connection to binomial coefficients. In Pascal’s triangle each number is the sum of the two numbers directly above it. Pascal's work on the binomial coefficients was to lead Newton to his discovery of the general binomial theorem for fractional and negative powers.
There are countless patterns you can uncover by looking at Pascal’s triangle.  It is used in Grade 7 to reinforce student's ability to identify patterns.

Pascal's Accomplishments

Pascal made important contributions in the natural and applied sciences, studying fluids, and clarified the concepts of pressure and vacuum.
Following Galileo and Torricelli, he disproved Aristotle's followers who considered the creation of a vacuum impossible and insisted that “nothing could not be something.” Pascal experimented on atmospheric pressure, proving that a vacuum existed. His results caused many disputes before being accepted. When Descartes visited Pascal in 1647, they argued about the vacuum which Descartes did not believe in. After his visit Descartes wrote about Pascal: “He has too much vacuum in his head.” When a year later Pascal observed that the pressure of the atmosphere decreases with height and assumed that a vacuum existed above the atmosphere, Descartes wrote about Pascal's experiments saying: “It was I who two years ago advised him to do it, for although I have not performed it myself, I did not doubt of its success...”
Pascal's other important scientific contributions include the derivation of the law or principle, which states that fluids transmit pressures equally in all directions, and his investigations in the geometry of infinitesimal. He insisted on empirical experimentation as opposed to analytical methods, and he believed that human progress was achieved by the increase of scientific discoveries resulting from such experimentation.

Mathematicians throughout History. The life of Blaise Pascal

Blaise Pascal was a French mathematician, physicist, inventor, and philosopher. He is considered one of the greatest minds in Western intellectual history.
Pascal demonstrated his abilities at a very early age. He was educated by his father, who decided that Blaise should not study mathematics before the age of 15 and all mathematics texts were removed from their house. Blaise however demonstrated immense interest towards it, starting to work on geometry himself at the age of 12 and proving himself a mathematical prodigy. He discovered that the sum of the angles of a triangle are two right angles and, when his father found out, he gave in and allowed Blaise a copy of Euclid.
At the age of sixteen, Pascal wrote his first essay that contained a number of projective geometry theorems, including Pascal's famous theorem about his mystic hexagon (if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the Pascal line of that configuration.)
Pascal was the inventor of the first mechanical calculator, a machine, very similar to mechanical calculator of the 1940s. In 1642-1645 he worked on it, in order to help his father with his work collecting taxes.
During the last years of his life Pascal abandoned his scientific work and devoted himself to Catholic philosophy and theology. He began to publish anonymous works on religious topics, eighteen Provincial Letters (published in1656 -1657). As scholars note, he treated the mysterious relations of human beings with God as if they were a geometrical problem.
Pascal's most famous work in philosophy is Pensées, a collection of personal thoughts on human suffering and faith in God (1656-1658). This work contains “Pascal's wager” which claims to prove that belief in God is rational with the following argument: “If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing.”
Pascal spent his last years helping the poor people and attending one religious service after another. Hel died at the age of 39. Controversy seemed to follow Pascal throughout his life. For example, Pascal offered a prize for a mathematical contest he proposed. However, he entered the answer under a pseudonym and crowned himself the winner.