Essential Knowledge Recap. Calculate the missing sides of these triangles.

30°

8

30°8

?

?

2000 year ago Archimedes asked:

for the most basic circle, with diameter 1,

what is the perimeter?

1

We call the perimeter of this, the most basic circle,

Pi (π)

Archimedes knew that π was less than 4.

How?

1

Why must the perimeter of the outside square be exactly 4?

1

He then drew a square inside the circle.

What is the perimeter of this circle?

1

So Pi (π) is between 2.83 and 4

Can we get closer?

1

This shape is closer to the perimeter of the basic circle.

How can we work out its perimeter?

1

What do we know about these triangles?

1

We can work out the opposite side using trigonometry.

1

So we now know that Pi is between 3.06 and 4.

Can we be more accurate?

1

Determine the

perimeter when the

circle is split into

10.

What about 20?

100?

1

In Summary

The most basic circle has a dimeter of 1.

We call its perimeter Pi (π)

Pi can never be written down.

We will never be able to work out all its digits because we would need to split the circle into an infinite number of parts.

So Pi goes on forever. It starts 3.14…

Numbers like this, that continue forever, are called irrational numbers.

2

What is the perimeter of a circle with diameter 2?

1

d

What is the perimeter of a circle with diameter d?

1

In Summary

The special name for the perimeter of a whole circle is circumference.

The circumference of any circle is Pi (π) × diameter

(C = πd)

Calculate the perimeter of each of these shapes.

23

3

Extension

If the whole circle has a diameter of 1, what is the perimeter of the black section?

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