A graphic method for drawing a regular pentagon inscribed in a circle using the geometric sketchpad

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From the characteristics of a regular pentagon, we know that each point is equivalent to a 360°/5 counterclockwise rotation of the previous point. Grasping this rule, we can use the iteration function of the geometric sketchpad to draw a circle inscribed For a regular pentagon, the specific operation is as follows:

Open the geometric drawing board, select the [Circle Tool] on the left sidebar, draw a circle O in the blank area of ​​the drawing board, and pick a point A on the circle O.

Double-click the center O as the center of rotation. Select point A, select the menu [Transform] - [Rotate], select Fixed Angle as the rotation parameter, then enter 360/5 in the box, then click the [Rotate] button to change the rotated point label to B. Use the line segment tool to connect points A and B to get line segment AB.

Select point A, execute the [Transform]-[Iteration] command, and click point B in the pop-up dialog box as the initial image. At this time, the screen displays the 4 sides of the iteration like a regular pentagon (because the system default number of iterations for non-depth iteration is 3). Click the [Show] button of the iteration box and select [Add Iteration]. (Or press ‘ ’ or ‘-’ on the keyboard). After adding 1 iteration, we can see that a complete regular pentagon is displayed. The number of iterations at this time is 4.

After completing all operations in the iteration dialog box, click the [Iterate] button to obtain a regular pentagon inscribed in a circle. The final effect is as shown in the figure.

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