Two days until the big day! Have fun celebrating with your students tomorrow.
Today’s activity uses Geometer’s Sketchpad to create pi. The link for the entire document with images can be found here: Pi Day Activity GSP. Enjoy!
A Recipe for Pi
|Open up GSP4 and select new from the File Menu. Maximize the screen.
|Use the Circle tool to create a circle. Click on the screen to create the circle. How far you drag determines the size – which can always be changed.
|Use the select tool to choose the circle you just made on the screen.
|Choose MEASURE from the grey toolbar at the top of the screen and then from the pull down menu select circumference.
|GSP will automatically measure the circumference of the circle. Since this is dynamic software, as you change the size of the circle, it will automatically change the measurement. Test this out by using the SELECT TOOL to grab the point on the circumference and move it around so that its size changes.
|Using the SELECT TOOL click on the CENTRE of the circle and the point on the CIRCUMFERENCE. The select arrow will turn sideways to let you know that you can select something. Then from the grey tool bar at the top of the page choose CONSTRUCT and from the drop down menu choose SEGMENT.
|That segment represents the radius. To measure the radius, use the SELECT TOOL to choose the line segment. Then from the grey tool bar at the top of the page choose MEASURE and from the drop down menu choose LENGTH.
|For this recipe for pi we need the diameter, the distance from edge to edge through the centre of the circle. To make the diameter, choose MEASURE for the grey toolbar at the top of the page and from the drop down toolbar, choose CALCULATE. This will activate the calculator.
|To make the diameter, the radius needs to be doubled. Select the measurement of the radius by clicking on it and it will automatically go into the CALCULATOR. Don’t type in the measurement. To multiply by two choose *(this means multiplication) and 2 then click on OK.
|Finally, choose MEASURE for the grey toolbar at the top of the page and from the drop down toolbar, choose CALCULATE. Use the calculator, and drag in the circumference of the circle, click on ÷ and click on the DIAMETER (radius x 2 that you just calculated) and then click on OK.
|At this point you should have pi π (approximately 3.14). Pi is the ratio of the circumference of a circle divided by the diameter. It is a constant and doesn’t change. To prove this, click on the point on the edge of the circle and drag it to make it larger and smaller. All of the other measurements should change as you change the size of the circle, but pi will remain the same!