Technology

Appreciation Art Teaching Technology

Math and Art: 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.

Application Challenge Technology

Creating Digital Landscapes

Tim Chartier, a professor of mathematics at Davidson college, has put together some great resources on using mathematical algorithms and free computer software to create random-looking 2D and 3D landscapes.

In the following paper posted at the MAA’s Digital Library, Chartier outlines the basic ideas of fractal geometry and random number generation, and creates a simple computer program that will generate random-looking coastlines and mountain ranges:

http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=1795

And in a follow-up blog post, Chartier takes the process one step further by turning his 2D fractal island into a planet, using free ray-tracing software.

http://forum.davidson.edu/mathmovement/2011/07/10/a-random-planet/

After explaining how to produce the planet, Chartier challenges the reader to create and submit their own!

It’s easy to see some of the applications of this idea in computer animation and graphics, as well as perhaps in simulations. A simple, innovative, and fun idea to explore!

By patrick honner, 13 years6 years ago

Appreciation Technology

Digi-Comp II: A Mechanical Computer

The folks at EvilMadScientist.com bring you a giant working replica of the Digi-Comp II, a 60s-era build-it-yourself computer kit:

http://www.evilmadscientist.com/article.php/dciivid

After the switches are initialized to choose the operation, the machine channels a stream of pool balls through various binary gates to effect addition, multiplication, and other basic mathematical and computational procedures. For more information, check out www.digi-compii.com.

As a pure math person, I never fully appreciated these mechanical computers. But after seeing things like the Digi-Comp, cam-based mathematics, and various mechanical calculators, I’m developing a genuine respect for them

By patrick honner, 13 years6 years ago

Appreciation Challenge 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, 13 years6 years ago

Appreciation Resources Student Work Teaching Technology

Student Work: Curvefitting With Geogebra

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.

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