On this web page you can use JavaSketchpad to construct daisy designs.
The basic daisy uses seven circles of the same size. Start with a single circle, as shown in this sketch, and then add six circles around it.
- Sequentially press buttons 1 through 6 to construct the other six circles. If you were using a compass, how would you know where to place the compass for each new circle?
- With a compass, you create circles of the same size by not changing the setting. In this sketch, how do you know all six circles are the same size as the starting circle?
- When you finish constructing the circles, color the petals of your daisy. Press Color the Daisy to see one possibility.
- Experiment by creating more daisies that touch or overlap. Use the red points at the centers of the starting circle and the first outer circle to move, change, and rotate the construction. Press Color the Daisy each time you want another daisy. Press X to erase the daisies and start over.
After constructing a daisy, you can use a straightedge to connect the petal tips. Depending on how you connect the tips, you get either a hexagon or a 6-pointed star. Follow the steps to explore both designs.
- Press Color the Daisy to see the daisy. This uses the same construction that you saw above.
- Press Show the Hexagon. How do you connect the petal tips to make the hexagon?
- Press Hide the Hexagon, then click Show the Star. How do you connect the petal tips to make the star?
- Can you connect the petal tips to create shapes other than a hexagon or a star? Explain your answer.
You can continue with more circles to construct a field of daisies. Press the buttons in this sketch to see the first circle, the middle circles, and the outer circles. For a more elaborate design, use your compass or geometry software to construct many more circles. Be creative when coloring your own field of daisies!