PASCAL'S TRIANGLE

-
Pascal's triangle ( An extraordinary logical structure )

Pascal's triangle is one of the most interesting structure in mathematics, named after the French mathematician, inventor, physicist Blaise Pascal ( 1623 - 1662 ).

 The structure looks like a triangle with 1 at the top vertex and running down the two slanting sides. This array of numbers is known as Pascal's triangle.

Also known as Meru Prastara, Tartaglia's triangle ( after Nicolo Tartaglia ).

Many other mathematicians studied the Pascal's triangle centuries before him in China, India, Germany, Italy and Persia.
PASCAL'S TRIANGLE



Features of Pascal's triangle
  • Expansion for the higher powers of binomial are possible by using Pascal's triangle.
    Example: The row for the index 5 in binomial expansion is
    1   5   10   10   5   1
  • The sum of the numbers in each row is the power of 2.
  • The numbers in each row is the power of eleven.
    Example: The first row is 11 to the power 0,
    2nd row the number is 11
    3rd row, the number is 121
    4th row, the number is 1331 etc.

Comments

Post a Comment

Popular posts from this blog

DOT PUZZLE ( CONNECT ALL THE DOTS WITHOUT LIFTING THE PEN AND WITH ONLY FOUR STRAIGHT LINES WITHOUT ANY OVERLAP )

-
Image
Here we would solve a dot puzzle Consider the figure below Connect all the dots without lifting the pen with only 4 straight lines and the lines do not overlap. Here are some examples already done for you but not been solved because some dots left to be crossed. You could see that some dots have been left to be crossed by the line. So do you think you could solve it. Let us try one more time. Now, what do you see, the puzzle has been solved with the required conditions. Find out some more solutions to this question.
Read more

EULER TRAIL PUZZLE

-
Image
What is an Euler trail ? An Euler trail ( Euler path ) is a trail in a finite graph which visits every edge exactly once. An Euler trail is a walk on the edges of a graph which uses each edge exactly once. Euler trail is also called an Euler chain , Euler walk , Euler path . Here is the puzzle as you could see in the picture. Your job is to cross each line exactly once without lifting your pen.  In the following figure consider every marked line as a single line and each must be crossed once without lifting you pen. Here are some examples already done, but in each case, one line is left ( marked red ) to be crossed . See the figures. Have you got the solution ? well, this is impossible to do however hard you try.  Explanation Consider the figure below and find the numbers of line reaching the centre of each box. In the figure you could see that there are three centre points with odd number o...
Read more