The Gardener's Circle
How can a gardener draw a perfectly round contour for a flowerbed?
Two stakes and a rope are enough: one stake is fixed at the desired position of the center of the flowerbed, one end of the rope is attached to the fixed stake, and the other end is attached to the second stake.
At this point, the gardener can mark the contour of the flowerbed using the free stake, moving around the fixed one while making sure that the rope is always taut.
Use the app below to create your virtual flowerbed using the gardener's method. The slider allows you to change the length of the rope.
Drag point P or the tip of the stake in the 3D View to create the flowerbed.
The 3D view can be rotated by dragging it with the mouse or using the predefined gestures for touch screens, and the buttons allow you to restore the 3D view to the original settings and delete the traces.
What common characteristic do all the points on the flowerbed's contour have?
In geometric terms, the contour of the flowerbed is a circle. How would you define the rope, using the same language?
If the gardener uses a rope that is 2 meters long, would a mushroom 3 meters away from the fixed stake be inside, outside, or on the contour of the flowerbed? What about a flower 1.9 meters away from the fixed stake? And a stone 2 meters away from the fixed stake? After writing down your answers, explain them using the language of geometry.