Linear Transformations with Graphics

I made this video when I was thinking about ways to teach the basics of linear transformations and matrices by illustrating their connections to computer graphics.  I wanted to show the actual matrix calculations that lead to the graphics, as well as a slider to show the graphics dynamically.  Since I made the video, GeoGebra added a spreadsheet, and it’s actually much easier and more versatile to do the same thing in GeoGebra (I’ll post that link soon).  However, it was a fun challenge to figure out how to push Excel to do graphics in this dynamic way.  To date, this is my most popular video on youtube.   Spreadsheet used in the video.

Multiplication Table

Making a multiplication table is an excellent beginning Excel Activity.  This video shows an efficient way to do it using absolute references, but there are many other approaches.   I use an open-ended handout for this activity in class.   This video is a good introduction to absolute references.   Spreadsheet used in the video.

Pool Table Math with Excel (includes a Video)

This is a classic problem solving activity that I first saw many years ago in Mathematics: A Human Endeavor.   The NCTM has a nice applet to test cases one at a time.  

Since I like playing with Excel and trying to extend what it can do, I wrote a spreadsheet to represent the problem.  The end result is much better than expected — this representation uses a slider to show many cases in a short period of time, and with it I noticed patterns that I never had before (e.g. if you start at (1,0) on a rectangle whose sides have GCD=2, you get a loop that goes through all squares). Read more >>

Excel for Math Classes

A video series.


Pascal’s Triangle

I was pretty excited when I figured out how to use conditional formatting in Excel to make a Sierpinski triangle.  I used very tiny cells, and then used conditional formatting to color in the cells corresponding to odd numbers in Pascal’s triangle.  The video also introduces Pascal’s triangle and explores some number patterns.  Spreadsheet used in the video (Excel 2003).

To do the conditional formatting in later versions of Excel, go to the Styles Group on the Home Tab.  Choose Conditional Formatting, and then choose New Rule.  Choose the last option, “Use a formula to determine which cells to format.”  Then enter the formula as in the video.