# Activity1 Pi the mathematical constant

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### Objectives

Students will be able to understand the value of Pi is ratio of circle's circumference to its diameter.

### Estimated Time

40minutes

### Prerequisites/Instructions, prior preparations, if any

Know the concepts of circumference and diameter of a circle.

### Materials/ Resources needed

Digital resources:Click here to open the file

Non digital resources:

- finding the perimeter of a circle using thread and diving it by using diameter.

### Process (How to do the activity)

- Click here for Finding Pi by Archimedes Method. Archimedes approximated the value of Pi by starting with the fact that a regular hexagon inscribed in a unit circle has a perimeter of 6. He then found a method for finding the perimeter of a polygon with twice as many sides. Applying his method repeatedly, he found the perimeter of a 12, 24, 48, and 96 sided polygon. Using the perimeter as an approximation for the circumference of a circle he was able to derive an approximation for Pi equivalent to 3.14. This video uses a somewhat simpler method of doing the same thing and carries it out to polygons with millions of sides. All that is needed to understand the calculation is knowledge of the Pythagorean Theorem.

Download this geogebra file from this link.

- Geogebra file for explaining how 'circumference / diameter' is a constant, denoted as pi (Greek letter), using a number line
- An animation of the same concept.

- Process/ Developmental Questions

Open the Geogebra file. Move the slider to 'unravel' the circumference' over the number line. Since the diameter is 1 unit (measuring from -0.5 to 0.5 on number line), the circumference ends at 3.14, showing the ratio between circumference

- Evaluation

- Question Corner

if the diameter is increased from 1 to 2, what will the circumference be?