2. Pascal’s Triangle and Fibonacci Numbers Andrew Bunn Ashley Taylor Kyle Wilson

3. PASCAL’S TRIANGLE The 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.

4. HISTORY Pascal didn’t discover the triangle, but he was the first to gather all the information together in 1653. The Chinese discovered it first, around the 2 nd century.

5. There are many number patterns in Pascal’s Triangle. PATTERNS

6. DIAGONALS Each diagonal of Pascal’s Triangle is a different number sequence.

7. HORIZONTAL Adding each horizontal of the Triangle results in a new pattern- the exponents of 2!

8. ELEVEN EXPONENTS Looking at each row as a number, we get the exponents of 11.

9. SYMMETRY Pascal’s Triangle is symmetric, except for the ‘spine numbers’, the middle numbers of every other row. These also correspond to the binomial coefficient theorem.

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

17. EVEN OUR FACES HAVE THE FIBONACCI SEQUENCE!

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

20. Serpinski’s gasket is a type of fractal.

22. Fin