Pascal's Triangle

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Pascal’s Triangle:

Pascal’s Triangle

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Pascal's Triangle is an arithmetical triangle you can use for some neat things in mathematics. 

A Brief History…:

A Brief History… Pascal was not the first to have discovered this triangle. Al- Karaji knew of the triangle during his lifetime(953-1029). Also was discussed by Omar Khayyam. (It is known as Khayyam’s triangle in Iran) Yang Hui discovered this triangle in China during his lifetime(1238-1298). (Known as Yang Hui’s triangle in China). Known as Tartaglia’s triangle in Italy (Tartaglia lived from 1500-1577). Pascal published his work in 1655.

Pascal’s work:

Pascal’s work Blaise Pascal published his paper with the help of Pierre de Fermat. In the paper he explained everything that he had discovered about the triangle. It starts with how to construct the triangle and then went on to list the 19 corollaries he found.

The Sums of the Row:

The Sums of the Row The sum of the numbers in any row is equal to 2 to the n th  power or 2 n , when n is the number of the row. For example: 2 0  = 1 2 1  = 1+1 = 2 2 2  = 1+2+1 = 4 2 3  = 1+3+3+1 = 8 2 4  = 1+4+6+4+1 = 16

Hockey Stick Pattern:

Hockey Stick Pattern If a diagonal of numbers of any length is selected starting at any of the 1's bordering the sides of the triangle and ending on any number inside the triangle on that diagonal, the sum of the numbers inside the selection is equal to the number below the end of the selection that is not on the same diagonal itself. If you don't understand that, look at the drawing. 1+6+21+56 = 84 1+7+28+84+210+462+924 = 1716 1+12 = 13

Triangular Numbers :

Triangular Numbers Triangular Numbers are just one type of polygonal numbers. See the section on Polygonal Numbers for an explanation of polygonal and triangular numbers. The triangular numbers can be found in the diagonal starting at row 3 as shown in the diagram. The first triangular number is 1, the second is 3, the third is 6, the fourth is 10, and so on

Thank You:

Thank You Made By: Akshit Aggarwal IX A

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