3rd Quarter

Pascals Triangle and Fibonacci NumbersAndrew BunnAshley TaylorKyle Wilson3rd QuarterMath Project 2012

Pascals TriangleThe Pascal patter is generated from the top. Start with a 1 and place two 1s on either side of it in the next row down. To construct further rows we continue to place 1s on the ends of each row while the internal numbers are obtained by the sum of the two numbers immediately above.History

Pascal didnt discover the triangle, but he was the first to gather all the information together in 1653.

The Chinese discovered it first, around the 2nd century.

There are many number patterns in Pascals Triangle.Patterns

DiagonalsEach diagonal of Pascals triangle is a different number sequence.Horizontal

Adding each horizontal of the Triangle results in a new pattern- the exponents of 2!Eleven exponents

Looking at each row as a number, we get the exponents of 11.Symmetry

Pascals Triangle is symmetric, except for the spine numbers, the middle numbers of every other row.These also correspond to the binomial coefficient theorem.

Fibonacci Sequence

When we add the rows horizontally, we get what is known as the Fibonacci Sequence.Fibonacci Sequence

Fibonacci Sequence in Nature

Even our faces have the Fibonacci Sequence!

Even and odd

Another pattern: if we shade the even and odd numbers differently, we get what is known as the Serpinski Gasket.

Serpinskis gasket is a type of fractal.

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