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1-Students will explore the number of pi by creating the polygons inscribed into a circle
2-Students will compute the angle between the vertices of the different polygons.

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1- computer
2-Geogebra software

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Directions:

Each student will work on their own computer. Please watch the YouTube video to lead construction.

1.   Create a circle that has center on the origin and radius of 5 units.

2.   Create an equilateral triangle that has all vertices on the circle

Create a point on the circle.

·         Then use “angle with given size ” tool to create a second point on the circle.

·         In this case, click on the point you created on the circle then click on the center point

·         When window pops up insert the degree of angle between the point and the point you will create. Since this figure is triangle, it has 3 sides therefore it will be 360/3=120o.

·         By using the “regular polygon tool ” create your equilateral triangle by clicking on the two points you have created and when a window pops up for the number of vertices, insert 3. Your equilateral triangle is ready.

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3.   Record the number of vertices and area for the polygon. Also write the formula for the area of the circle.

| # of Vertices/Sides | Area | Formula for Circle Area (r=5) | Guess for π
| 3 |   | 25 π |
| 4 |   | 25 π |
| 5 |   | 25 π |

4.   Create square with the same way you created triangle. Keep in mind that each time the number of vertices and the degree between vertices will change. Once you create your square, record it to your table.

5.   Create pentagon with the same way you created triangle. Keep in mind that each time the number of vertices and the degree between vertices will change. Once you create your square, record it to your table.

6.   When we increased the number of vertices, what do you observe for the figures inside the circle?

7.   What is your guess for π for the decagon? What do you think would it be for 100 th figure?

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You will be able to explore the number of pi by creating polygons inscribed into a circle.