Invariance and Change in the circle
Task
Use the radius slider to change the radius and therefore the size of the circle. Look for invariance and change by asking ‘what changes and what stays the same’ as you move the slider. Make a conjecture based on your observations.
Then use the angle slider to change the angle of the sector. What size of angle is needed to make the length of the arc equal to the radius?
What size angle is needed to make the arc length equal to 3 x radius? Or 7 x radius? What do you conjecture?