Discovering Pi
In this activity you are going to investigate the relationship between the perimeter of regular shape and the length of the longest diagonal across that shape.
To start with, the shape is a square, and the diagonal is given. The ratio is calculated by doing perimeter ÷ length.
Grab points A and B, and move them around. What do you notice about the perimeter and length? What do you notice about the ratio?
Reset the activity, and use the slider to change the shape to a regular hexagon. In the input box, change "Segment[B,D]", so that D is replaced by the point furthest away from B. Again grab points A and B, and change the dimensions of the hexagon.
What do you notice?
Investigate what happens as you increase the number of sides in the regular polygon.
You can zoom out by right clicking on the background when nothing is selected. You can move the position of the screen using the arrow keys. To type a subscript in the input box, type A_1.
To start with, the shape is a square, and the diagonal is given. The ratio is calculated by doing perimeter ÷ length.
Grab points A and B, and move them around. What do you notice about the perimeter and length? What do you notice about the ratio?
Reset the activity, and use the slider to change the shape to a regular hexagon. In the input box, change "Segment[B,D]", so that D is replaced by the point furthest away from B. Again grab points A and B, and change the dimensions of the hexagon.
What do you notice?
Investigate what happens as you increase the number of sides in the regular polygon.
You can zoom out by right clicking on the background when nothing is selected. You can move the position of the screen using the arrow keys. To type a subscript in the input box, type A_1.
Discovering Pi
Created with GeoGebra 
Ideas for Teachers
This investigation starts by discovering that ratios within regular shapes are always the same, and leads to a discussion as the polygon approaches a circle. Allowing the pupils to play around on this activity is ideal, maybe setting it as a homework to discuss in the next lesson. Alternatively, get them to create the activity themselves using GeoGebra, in order to perform the investigation.
This investigation starts by discovering that ratios within regular shapes are always the same, and leads to a discussion as the polygon approaches a circle. Allowing the pupils to play around on this activity is ideal, maybe setting it as a homework to discuss in the next lesson. Alternatively, get them to create the activity themselves using GeoGebra, in order to perform the investigation.
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