Links to Sites With More Information
About Numbers and Patterns
There are many sites on the World Wide Web with information about Arithmetic Sequences, Pascal's Triangle and Triangular Numbers. Below are a few links that you can use to learn more about these patterns of numbers.
Arithmetic Sequences
Arithmetic Sequences Mini-Lessons
This site contains a video lecture about Arithmetic Sequences. It also contains a set of exercises that test understanding. There are technical exercises, applications exercises, technology exercises (which use a graphing calculator), and "in your own words" exercises (questions that require an answer to a question with words, rather than calculations).
Arithmetic and Geometric Sequences
This site discusses the difference between arithmetic and geometric sequences and why the terms "arithmetic" and "geometric" are used to define these special sequences of numbers.
This site uses Excel worksheets to explore the properties of graphs of Arithmetic Sequences and compares them to the graphs of Geometric Sequences.
Pascal's Triangle
Number Patterns in Pascal's Triangle
This site is rich in information about patterns in Pascal's Triangle. It includes patterns that have to do with powers of 2, the Fibonacci Sequence, Triangular Numbers, the Sierpinski Fractal, and more.
Lessons on Pascal's Triangle for Teachers
This is a site for teachers with lessons about Pascal's Triangle at an elementary, intermediate and advanced level. Each level includes a Discovery Lesson and Student Worksheets.
Graphic Patterns in Pascal's Triangle
This page has excellent graphics showing patterns that can be found in Pascal's Triangle. It relates those patterns to information about prime numbers. It also has an applet that allows you to display 256 rows of Pascal's Triangle.
Pascal's Triangle and Polynomials
This site discusses Chebyshev Polynomials and Mobius Transformations whose coefficients are taken from slices of Pascal's Triangle. The site contains sophisticated mathematics suitable for college students.
Lesson on Pascal's Triangle for Grades 5 and Up
This site presents a lesson designed to enable students at grade 5 or higher to recognize the integers, rows and columns that comprise Pascal's Triangle. The main objective of the lesson is to enable students to reproduce the first eleven rows of Pascal's Triangle by recalling number patterns given in the lesson without having to look again at the original triangle.
Using Pascal's Triangle in Algebra and Probability Problems
This site discusses the role of Pascal's Triangle in Algebra and in Probability/Combinatorics. In particular it shows how Pascal's triangle can be used to find the coefficients of polynomials that result from binomial expansion.
Triangular Numbers
Number Patterns and Triangular Numbers
This page has a brief explanation of Triangular Numbers and shows some patterns that can be used to prove number theory formulas.
Pascal's Triangle and Triangular Numbers
This page provides some basic information about Triangular Numbers and relates them to a column in Pascal's Triangle.
Applications of Triangular Numbers
This page gives some advanced applications of Triangular Numbers suitable for students in high school algebra.
Perfect Squares and Triangular Numbers
This page explores the problem of identifying all the Triangular Numbers that are also perfect squares. The discussion involves elementary Number Theory, and is suitable for college students.
email the author: Bruce Jacobs
Last modified: Thursday, February 6, 2003