Sunday, September 19, 2010

What is Pascal's Triangle?

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in Greece, India, Persia, China, and Italy.[1]

The rows of Pascal's triangle are conventionally enumerated starting with row 0, and the numbers in each row are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number directly above and to the left with the number directly above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

This construction is related to the binomial coefficients by Pascal's rule, which states that if

(x+y)^n=\sum_{k=0}^n{n \choose k}x^{n-k}y^{k}

then

 {n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}

for any nonnegative integer n and any integer k between 0 and n.

Pascal's triangle has higher dimensional generalizations.



Wednesday, September 15, 2010

Is Astrology considered as a Science?

Astrology, a system based on the belief that the stars, planets, and other heavenly bodies affect human affairs.

Does this word, ASTROLOGY, maybe considered as a science? After I heard that word, I first thought that this is considered as a science but after some researches I found out that ASTROLOGY is a pseudo science from the prefix PSEUDO meaning false.

Astrology only pretends to be a science. Over many centuries, some researchers used to research such just to prove that astrology is science but still they failed to prove it.

Let me site an example for us to understand it further. Do you think it may comfort us to believe that the manager of the company I applied for, rejected me because of the motion of the stars, the moon, and the planets along the zodiac rather than to admit that I behaved badly during our interview.

It only proves us that that our life does not depend on what the motion of the sun, the moon, the planets and the other heavenly bodies but our life depends on us. We are the manipulators of our own life.