Technology

Pendulum Wave Animation

Inspired by a video showing the seemingly chaotic movements of pendula of varying lengths, I created this animation in Geogebra.

Using sine functions of varying periods, I was able to create a set of points that oscillate in a manner similar to the pendula in the “Pendulum Waves” video.

Consider the point on the bottom as the timekeeper. In the the time it takes the bottom point to complete one full trip (from center to right to left back to center), the next point up completes two full trips; the point above that three full trips, and so on.

Since every point is completing a whole number of trips in that amount of time, they will all sync up every time the bottom point is ready to start again. And watch the “even” points to see when they sync up, too!

By patrick honner, 15 yearsJune 19, 2011 ago

Appreciation Resources Student Work Teaching Technology

Student Work: Curvefitting With Geogebra

Here is some student work from a recent project I conducted on fitting curves to images in Geogebra. The details of the assignment can be found here, and more examples of student work can be seen on my Facebook page.

Students were asked to find pictures and use Geogebra to fit trigonometric curves to the images using transformations. Here are some of the results.

Smart Water = Smart Curves

My Good-Looking Windowsill

Sine of Camel Humps

Overall, I was really impressed with the creativity the students showed, and their facility with fitting these curves to the forms! A mathematical and artistic success in my book.

Resources Teaching Technology

Curvefitting With Geogebra

Inspired by some of my own forays into curvefitting with Geogebra (the squash at the right, or my Sine Waves on the Beach), I’ve created a student project built around the idea.

Finishing up a unit on trigonometry with graphs of trigonometric functions, it occurred to me that I have never really been comfortable teaching transformations. I think part of the reason is that it’s hard to get your hands dirty, play around, and develop intuition with this topic. This is where Geogebra comes in!

The project essentially works like this:

1) Students find an image, preferably one they capture themselves

2) Students paste the image into Geogebra

3) Students graph a relevant trigonometric function and play around with the various parameters (like period, amplitude, phase shift) until the curve fits the image

4) Students can use domain restrictions, and some of Geogebra’s aesthetic features, to polish everything up.

The first run of this project has produced some great results! You can see some sample student work here, and more on my Facebook page.

Resources Technology

Library of Visual Manipulatives

This is another terrific resource: the Library of Visual Manipulatives from Utah State University.

http://nlvm.usu.edu/

There are one hundred or so simple, interactive programs available spanning Algebra, Geometry, Numbers and Operations, Measurement, and Data. And everything is sorted by appropriate age level. There are certainly a lot of interesting activities to navigate through here.

I’d say this is NSF money well-spent.

By patrick honner, 15 yearsApril 9, 2011 ago

Geometry Resources Technology

Toothpick Sequences

This is a cool applet that allows you to explore various fractal “toothpick sequences”:

http://www2.research.att.com/~david/oeis/toothpick.html

A number of options allow the user to look at variants of the object, zoom in, change iteration parameters, and change the underlying sequence. Click the Introduction button for a short overview.

Not sure what ATT Research plans to do with this, but it’s fun to play around with!

By patrick honner, 15 yearsApril 7, 2011 ago

Pendulum Wave Animation

Student Work: Curvefitting With Geogebra

Curvefitting With Geogebra

Library of Visual Manipulatives

Toothpick Sequences

Follow Mr Honner