Mathematics Pascal’s Triangle

14
Mathematics Pascal’s Triangle Date 22.10.13 James McKee

TAGS:

description

Mathematics Pascal’s Triangle. Date 22.10.13 James McKee. Challenge overview. What is Pascal’s triangle?. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1. Challenge overview. What is Pascal’s triangle? - PowerPoint PPT Presentation

Transcript of Mathematics Pascal’s Triangle

Page 1: Mathematics Pascal’s Triangle

MathematicsPascal’s Triangle

Date 22.10.13

James McKee

Page 2: Mathematics Pascal’s Triangle

2

Challenge overview

What is Pascal’s triangle? 1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 3: Mathematics Pascal’s Triangle

3

Challenge overview

What is Pascal’s triangle?

What patterns can you spot?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 4: Mathematics Pascal’s Triangle

4

Challenge overview

What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 5: Mathematics Pascal’s Triangle

5

Challenge overview

What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 6: Mathematics Pascal’s Triangle

6

Challenge overview

What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

Joke:

Q. What does the B in Benoît B Mandlebrot stand for?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 7: Mathematics Pascal’s Triangle

7

Challenge overview

What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

Joke:

Q. What does the B in Benoît B Mandlebrot stand for?

A. Benoît B Mandelbrot

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Page 8: Mathematics Pascal’s Triangle

8

Challenge overview

Class experiment: coin tossing.

Come to the Science Festival to see a Galton board.

Challenge: understand the connection with Pascal’s triangle.

Page 9: Mathematics Pascal’s Triangle

9

Challenge overview

Class experiment: biased coin tossing.

Is the first digit after the decimal point of sin(n) even or odd?

Challenge: understand the connection with Pascal’s triangle.

Page 10: Mathematics Pascal’s Triangle

10

Curriculum links

Number Spot patterns

Use decimal numbers

Divisibility: odd or even

Page 11: Mathematics Pascal’s Triangle

11

Curriculum links

Statistics Design experiments

Appreciate the concept of bias

Page 12: Mathematics Pascal’s Triangle

12

Added value

Support and feedback from enthusiastic Royal Holloway staff.

Page 13: Mathematics Pascal’s Triangle

13

Added value

Support and feedback from enthusiastic Royal Holloway staff.

Come to Super Science Saturday and play with a Galton Board.

Page 14: Mathematics Pascal’s Triangle

Questions?


Pascal’s Triangle - Lee Fothergill · Pascal’s Triangle 1628-1662 . Pascal’s Wager Even though the existence of God cannot be determined through reason, a person should wager

Pascal’s Triangle - Lee Fothergill · Pascal’s Triangle 1628-1662 . Pascal’s Wager Even though the existence of God cannot be determined through reason, a person should wager

7.2 Pascal’s Triangle and Combinations 4/10/2013.

7.2 Pascal’s Triangle and Combinations 4/10/2013.

PASCAL’S TRIANGLE. * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

PASCAL’S TRIANGLE. * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

Counting III: Pascal’s Triangle, Polynomials, and Vector Programs

Counting III: Pascal’s Triangle, Polynomials, and Vector Programs

Mathematics in Ancient Chinawilliams/Classes/300F2011/PDFs... · 2011-09-27 · – Pascal’s triangle (350 years before Pascal) – Solution of simultaneous equations using matrix

Mathematics in Ancient Chinawilliams/Classes/300F2011/PDFs... · 2011-09-27 · – Pascal’s triangle (350 years before Pascal) – Solution of simultaneous equations using matrix

Pascal’s Triangle and Expanding Binomial Powersvegalee.weebly.com/.../f11u_se_section_6_3_pascal_s_triangle.pdf · Pascal’s Triangle and Expanding Binomial Powers It is widely

Pascal’s Triangle and Expanding Binomial Powersvegalee.weebly.com/.../f11u_se_section_6_3_pascal_s_triangle.pdf · Pascal’s Triangle and Expanding Binomial Powers It is widely

Induction in Pascal’s Triangle - University College Cork...Induction in Pascal’s Triangle Pascal’s Formula, The Hockey Stick, The Binomial Formula, Sums Pascal’s Triangle:

Induction in Pascal’s Triangle - University College Cork...Induction in Pascal’s Triangle Pascal’s Formula, The Hockey Stick, The Binomial Formula, Sums Pascal’s Triangle:

Combinatorial Enumeration in Pascal’s Triangleramanujan.math.trinity.edu › bmiceli › research › MajorsS16.pdf · Combinatorial Enumeration in Pascal’s Triangle How To Count

Combinatorial Enumeration in Pascal’s Triangleramanujan.math.trinity.edu › bmiceli › research › MajorsS16.pdf · Combinatorial Enumeration in Pascal’s Triangle How To Count

Quantum Pascal’s Triangle and Sierpinski’s carpet · Quantum Pascal’s Triangle and Sierpinski’s carpet Tom Bannink bannink@cwi.nl Harry Buhrmanz buhrman@cwi.nl August 2017

Quantum Pascal’s Triangle and Sierpinski’s carpet · Quantum Pascal’s Triangle and Sierpinski’s carpet Tom Bannink [email protected] Harry Buhrmanz [email protected] August 2017

Making Money From Pascal’s Triangle John Armstrong King’s College London.

Making Money From Pascal’s Triangle John Armstrong King’s College London.

K Pascal’s Triangle and K Fibonacci Sequence · Combining Theorem 15 with the same argument as in Pascal’s triangle (mod p), we conclude that the 3 Pascal’s triangle (mod p)

K Pascal’s Triangle and K Fibonacci Sequence · Combining Theorem 15 with the same argument as in Pascal’s triangle (mod p), we conclude that the 3 Pascal’s triangle (mod p)

7.2 Pascal’s Triangle and Combinations

7.2 Pascal’s Triangle and Combinations

Pascal’s Triangle - UMBCcampbell/MEPP/Pascal-Triangle/Pascal... · 2014. 5. 6. · The numbers in Pascal’s Triangle are called: Binomial Coefficients Choose numbers The number

Pascal’s Triangle - UMBCcampbell/MEPP/Pascal-Triangle/Pascal... · 2014. 5. 6. · The numbers in Pascal’s Triangle are called: Binomial Coefficients Choose numbers The number

Jacobsthal Decompositions of Pascal’s Triangle, Ternary · PDF filePascal’s Triangle, Ternary Trees, andAlternating Sign Matrices Paul Barry School of Science Waterford Institute

Jacobsthal Decompositions of Pascal’s Triangle, Ternary · PDF filePascal’s Triangle, Ternary Trees, andAlternating Sign Matrices Paul Barry School of Science Waterford Institute

Exploring Pascal’s Triangle - Math circlemathcircle.berkeley.edu/sites/default/files/BMC6/pdf0607/pascal.pdfMore rows of Pascal’s triangle are listed on the final page of this

Exploring Pascal’s Triangle - Math circlemathcircle.berkeley.edu/sites/default/files/BMC6/pdf0607/pascal.pdfMore rows of Pascal’s triangle are listed on the final page of this

Permutations Combinations Pascal’s triangle Binomial Theorem

Permutations Combinations Pascal’s triangle Binomial Theorem

Blaise Pascal and Pascal’s Triangle. PASCAL’S TRIANGLE * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

Blaise Pascal and Pascal’s Triangle. PASCAL’S TRIANGLE * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

Quit Permutations Combinations Pascal’s triangle Binomial Theorem.

Quit Permutations Combinations Pascal’s triangle Binomial Theorem.

Choose Multichoose - Lehigh Universitygi02/Boca16b.pdf · Choose Triangle Recall ‘Pascal’s Triangle’ 1650 Kayyam’s Triangle 1000; Yang Hui’s Triangle 1350, ..... Display:

Choose Multichoose - Lehigh Universitygi02/Boca16b.pdf · Choose Triangle Recall ‘Pascal’s Triangle’ 1650 Kayyam’s Triangle 1000; Yang Hui’s Triangle 1350, ..... Display:

Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.

Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.