| Title | Description |
|---|---|
| Pascal's Triangle Applet | An applet which shows Pascal's Triangle and plays out various animations to demonstrate the properties of Pascal's Triangle. |
| Pascal's Traingle Geogebra Applet | Applet showing Pascal's triangle allowing for a variable number of rows with coloring available for numbers that are a multiple of a selectable n. |
| Pascal's Triangle | This is a interactive activity allowing you to fill in the entries of Pascal's triangle, and (on other pages) color in different modulus' within the triangle. |
| Coloring Multiples in Pascal's Triangle | This website 'rolls' a random value and asks you to color in the numbers of pascals triangle that are a multiple of that rolled number. |
| Pascal's Triangle and Binomial Expansion | This interactive website has students use Pascal's Triangle (with entries missing that you can drag into the appropriate spot within the triangle)to expand polynomials as a set of Challenge Quizzes. |
| Patterns in Pascal's Triangle | This webpage generates a lesson plan based on the Standard Addressed and The Textbook Alighment. It also leads to the interactive activity examples. |
| Title | Description |
|---|---|
| Pascal Triangle Web Sources | A collection of links Applets related to Pascal's Triangle |
| Math Forum Internet Mathematics Library | A collection of links to Applets and websites for a huge variety of mathematics and statistics topics facilitated by The Math Forum at NCTM, including Pascal's Triangle |
| Pascal's Triangle and Binomial Expansion | This is a small collection of applets on cK-12 related to Pascal's Triangle and Pascal's Pyramid |
| Cut the Knot | Includes a wide variety of applets and other web based links regarding Patterns in Pascal's Triangle. Includes a method of generating the Catalan Numbers from Pascal's Triangle. |
| Boston University: Teaching Notes for the Patterns in Pascal's Triangle Problem | Includes a wide variety of applets and other web based links regarding Patterns in Pascal's Triangle. Most of these links go to handouts, not applets, but I thought this still seemed to count. |
| Title | Type | Description |
|---|---|---|
| OEIS | Website | The Online Encyclopedia of Integer Sequences; a website allowing users to search for sequences of integers, which will be particularly be useful (as it was for me) to discover the sequence of Catalan numbers for the first time. |
| Series and Sigma Summation Notation | Video | An introduction (or for the students in our class, a detailed review) to the concept of series, and writing finite and infinite series using sigma notation. While this video is great, it is likely not necessary to be watched in it's entirety by the students in our Math 5010 course. |
| Khan Academy: Intro to the Binomial Theorem | Video | An overview of the Binomial Theorem presented as a lecture with examples. |
| Khan Academy: Pascal's Triangle and binomial expansion | Video | As a suplement, see Khan Academy: Binomial Expansion and Combinatorics |
| Khan Academy: Binomial Probability example (10:23) + Generalizing k scores in n attempts (4:12) | Video | As a highly recommended supplement, see Khan Academy: Combination formula |
| Wikipedia: Catalan Numbers | Website | A wikipedia page detailing the Catalan numbers. See especially Applications in Combinatorics, number of monotonic lattice paths along the edges of a grid with n × n square cells, which do not pass above the diagonal, and Second Proof (very straightforward, relatively easy to understand) |
| Website: The Catalan Numbers | Website: Article | Medium article detailing The Catalan Numbers with historical background and examples. |
| Generalized Binomial Coefficients | Website | A website noting both the 'typical' and generalized binomial coefficient formulas. See especially equations for (3) and (4). |
| Binomial Series | Video | This is a video by The Organic Chemistry Tutor where they explains how to use the binomial series to represent a function as power series in sigma notation or summation notation. It is CRUTIAL that we go over the example at 30:45 for 1 over the square root of 1-x. |
| Taylor series: Binomial Series 1 | Video | This is a video by DaveAcademy going through the derivation of the Binomial Series as a Taylor Series. |
| Pascal's Triangle | Website | Published by Math is Fun, this site details some of the properties of Pascal's triangle in an easy to understand way. |
| Dear Colleague Letter | Article | An Overleaf LaTeX document compiled for Math 4400 in the Spring of 2020, detailing the original problem (and importantly, solution) which inspired this entire project. |