Case Study Y
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Below is an HTML copy of the worksheet given to pupils for the LOGO activity in Case Study Y.
The aim of this activity is to estimate the value of p (pi) by experiment.
To estimate a value of p, we could draw a circle, measure the circumference C and diameter D, and divide C by D. The value should be approximately 3.
Method for experiment
Then we could move the pointer across the middle of the polygon using the FORWARD and BACKWARD commands until we reach the other side .
If we had to move forwards 46 to reach the other side then our “diameter” is 46.
To estimate p, we divide 140 by 46, giving 3.043.
Procedure for experiment
Draw a table like the one below, and record your results as you go along.
|Number of sides N||Length of sides L||“Circumference” C (=LxN)||“Diameter” D||Estimate of PI (=C/D)|
|5||30||5 x 30 = 150||...||...|
|5||40||5 x 40 = 200||...||...|
|6||25||6 x 25 = 150||...||...|
As the number of sides increases, the polygons will look more and more like circles, and the estimates for PI should get more accurate.
The procedure for drawing a polygon is available on the system already.
When it is loaded, the polygon command is used as follows:
polygon N Swhere N is the number of sides and S is the length of each side.
The pointer will be left facing across the centre of the polygon.
To help you judge the distance across the middle, there is another command:
scale N LThis draws a scale below the pointer with N sections, each of length L.
For example, the commands scale 10 10 and polygon 7 20 would produce the output shown on the right.