## The Geometer's Sketchpad Modeling a Ferris Wheel

### by Jim King

Modeling a Ferris Wheel

## Using Translations and Animation

Physical devices can be modeled using dynamic geometry. A vital tool for moving objects around in the model are the isometries, or distance-preserving transformations. This model of a Ferris wheel provides a good example.

### Begin with a circle and a template for the chair.

• Start a new sketch and draw a circle; then add point C as a Point on Object that slides around the circle.

• Also, create a chair-shaped blob as a Polygon Interior.

### An animation button for C.

• We wish to animate C so that it runs around its circle. Select the point C and also the circle (by shift-clicking).

• Now we choose an item on a submenu. Press the mouse button down on the Action Button Item of the Edit menu and then slide the mouse to the right and down to choose Animation....

• You will get a dialog box with some choices. This time just click on the button that says Animate.

• An animation button appears in the sketch. Double-click on the button to send the point C running around the circle.

• To stop the animation, click with the mouse anywhere in the sketch (you may have to hold down the button a while to get the animation to stop).

• Add a segment. Construct the radial segment AC and double-click the animation button again. What happens to the segment?

### Attach a chair at point C using a translation.

• We will mark a vector from a vertex of the blob to point C. Select one on the vertices of the blob and then point C. Now choose Mark Vector .

• Translate the blob by the marked vector. Where does the blob move? What happens when you drag point C. Why?

• Now double-click the animation button again. What happens? Why? In the figure, can you tell which vertex on the blob was selected when marking the vector?

This Ferris wheel has just one seat. Let's add more seats. We will do this by constructing 3 more points on the circle to which we will attach the seats. These points, along with C, will make four points, equally spaced 90 degrees apart around the circle.

• Construct these points by constructing the line AC and then the line through A perpendicular to line AC. The points of intersection of these lines with the circle are the four equally spaced points.

• Run the animation again to see how the four points move in unison. Hide the two lines for esthetic reasons.

• Now in turn mark the vector from the same vertex of the blob as before to each of these three new points. Each time you mark a vector, translate the blob by this vector.

• Now double-click the animation button again to see your Ferris wheel.

### Refinements and Extensions.

• Adjustable seats. Since this construction is dynamic, we can make changes. Drag some vertices of the original blob to reshape the "seat." Can you make the seats face the opposite way as before?

• A three-seater. Make another Ferris wheel with three seats.