Before trying the challenge, your students and you should read this section. You can take the activity apart, which is the power of Squeak. Click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 1024x768 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. Again, taking it apart and even breaking it is a good way to learn. No matter how bad a mess you make, you can always get back to the original activity by exiting Squeak and starting over, so don't worry. This activity is written using a computer language called Smalltalk, so understanding the simulation will be much more challenging.

Challenge: You may think mathematics and art aren't related, but nothing could be farther from the truth. The sense of beauty you see in art is equally important in mathematics. Symmetry is part of beauty and it runs throughout art and mathematics. Theorems have a sense of beauty because they represent truth. Beauty gives you a sense of balance and well-being in your life. The Squeak project was organized on the page to be functional and that often leads to a kind of beauty. But beauty is in the eye of the beholder, so we challenge you to recreate the Squeak Exercise Challenge project in a way that leaves you with a sense of balance and beauty. With the tools in Squeak, you can make your own drawings. Any of the objects can be moved and resized and their colors can often be changed. Click on any object while holding down the alt key on a PC or the command key on a Mac and you will see the halo of handles. Click on the red handle at the upper left to explore many options for changing the object. Go to Squeakland for tutorials and more information on using Squeak. When you are done go to the NASA CONNECT web site to submit your version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open your project.

Super Challenge: Do your students know trigonometry and how to program? Then this challenge is for them! Have them modify the simulation so it displays hour lines at the local clock time. The angle of the hour line for the horizontal sundial simulation is calculated from an equation that is relatively simple, but needs correction if they want the local clock time as read on your watch. The equation is tan HL = tan h * sin L, where HL is the angle of the hour line, h is the hour angle calculated by multiplying the number of hours away from noon by 15 and L is the latitude. The time indicated on a horizontal sundial that is built using this equation is called apparent solar time. Your students can learn how to obtain the standard time or local clock time that they would read on their watch at http://perso.wanadoo.fr/blateyron/sundials/gb/heure.html. They can obtain the Equation of Time correction at http://www.sundialsoc.org.uk/glossary/equations/equations.htm.

The script for this Squeak activity had to be written in Smalltalk because the graphical tiles don't have trigonmetric functions. The script called angle, which calculates the angle of the hour line, is below.

For this script, THA is the tangent of the hour line angle, Head is the heading of the hour line used to display the blue line in the simulation and Rad is used to convert between degrees and radians. Smalltalk uses radians as a angle measure, which is true for many programing languages. Your students will need to define a variable for longitude. Use the Options Menu in the Viewer to define a variable (see Squeak Etoy Quickstart Guide). Then they need to add a watcher to allow users to enter their longitude for the longitude correction. Finally, they will have to modify the script above to include the longitude and Equation of Time corrections. It is likely that they don't know how to program in Smalltalk. However, looking at the above script, making modifications and using trial ans error, they can determine how the program works and learn how to make the needed modifications.