## The Geometer's Sketchpad Spirograph Lab, Part 3

### Mike Riedy

TOC || Page 2 || Page 3 || Page 4 || Intro Lab

### Part 3: Circles On Circles

Preferences:

Since we are going to be taking measurements, everyone's computer needs to be set to the same units. Go to the "Preferences" window under the DISPLAY menu. When yours look exactly like the ones shown below, click "OK". Now we can all be consistent when we start taking measurements.

In future labs you should get in the habit of setting the preferences of GSP as one of the first things you do. You don't know who was using the computer before you and he may have been a complete and utter lunatic.

Spirographs:

This is the heart of the lab. The following construction can be tricky, but stick with it. If you get lost or confused go back and reread the directions.

Start with a new sketch. Go back to page one and do another Roger construction. Now draw a smaller circle in the lower right corner of the screen. Label the point on the circle "Radius control 2". Have the computer put a new point on the circle by highlighting the circle and choosing "Point On Object" from the CONSTRUCT menu. Change the label on the new point to "Bert".

Bert and Roger are friends and are going to work together to make wonderful things happen. Save this sketch at this point in case anything weird happens. Save the sketch as "Roger and Bert".

Here's the tricky part. Highlight the center of Bert's circle, and the point Roger, in that order. Go to the TRANSFORM menu and choose 'Mark Vector "Roger"'. The question mark represents the name of the point of the center of Bert's circle. Since it could be different for different people, we will just call it "?".

If you did this correctly you should see an arrow-like thing shoot out toward Roger. Don't worry, Roger will be okay.

Now highlight Bert and his circle but not the center or the point Radius control 2 . Choose "Translate" from the TRANSFORM menu and a box like the one below will appear.

Before clicking "OK" make sure that the "By Marked Vector" circle is selected. If you have done everything correctly, when you click "OK" a new circle and a new Bert will appear around Roger.

What label does the computer give to the new point on the circle around Roger?

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Change whatever label the computer gives the new point to "Son of Bert". Notice when you move Bert around his circle that Son of Bert also moves around his circle, and vice versa.

Measure and record the distance from Roger to the center of his circle:

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Measure and record the distance from Bert to the center of his circle:

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Highlight the following objects in the following order (order is very important).
1. Bert
2. Bert's circle
3. Roger
4. Roger's circle

Choose "Animate" from the sub-menu under the "Action Button" under the EDIT menu. Make sure your choices for the animation match those in the picture above. Once again, the names of the circles are not important, but the "one way" and "quickly" are crucial.

Once your screen matches the one above, click on "Animate". A button should appear on your sketch labeled "Animate". Change the label on the button to "Spirograph".

Highlight Son of Bert and choose "Trace Point" from under the DISPLAY menu. Change the color of Son of Bert to blue and double-click on "Spirograph".

Describe what you see:

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Save this sketch by choosing "Save" from the FILE menu. Since you have already saved the sketch, the computer will save your spirograph machine over the sketch previously saved as "Roger and Bert" at the bottom of page 2.

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