# Pi Day 2018

Happy Pi Day 2013, this interactive activity will guide you through ways to find π using polygons.

Most people know the definition of PI as the ratio of the circumference of a circle to its diameter. They have probably used PI in circle problems, calculating the area using ``` area = πr2 ``` or the circumference using `C = 2πr` or `C = πd` . But what of this mysterious number, is it possible to create a visual analogy. This demonstration attempts to do so by examining and manipulating a regular polygon.

This will be done in two ways firstly by considering the perimeter of a regular polygon which fits perfectly in a circle of radius one, the polygon can be opened to form a straight line and its perimeter then measured. To show how π relates to area we again use a polygon, dividing its area into triangles.

## The controls

For the sake of consistency with the other activites the controls are described below. But the best way to use this activity is to follow the instructions guide in the top right hand corner

• Next button is pressed to move to the next instruction
• Previous button is pressed to move back to the previous instruction
• Focus select the part to focus and zoom in on
• Area toggle area or circumference
• Exterior angles toggle to display exterior angles
• close polygon click button to animate the polygon closing
• open polygon click button to animate opening the polygon
• Exterior Angle Adjust this slider to change the exterior angle which in effect opens or closes the original polygon
• side length Adjust this slider to change the side length
• side length Adjust this slider to change the number of sides.
• Automatic recalculate - when this button is on changing the number of sides and the two other sliders will automatically adjust the angle and length to form a regular polygon that fits perfectly in the circle.

## Related Activities

If you like visual mathematics why not check out the interactive multiplication tables The inspiration for this activity actually came from playing around with the interactive fractal after setting the branches to one. The interactive polygon explorer. is better for teaching the various properties and angles of polygons.

Angle
Exterior angle of the polygon.
Length
Control the Length of each side
Sides
Control the number of sides the polygon.
Auto
Calc
Length and angle are calculated for a regular polygon inside the circle
<<
Animate close the polygon
>>
Animate open the polygon
Exterior
Toggle display of the exterior angles
Area
Toggle to display triangles inside polygon
Select zoom area
Instruction use the buttons below for next and previous
Next
Next Instruction
Prev
Previous Instruction