Circle Terminology: A circle is one of the most basic shapes.

It is basic enough for my 3 year old daughter to draw.

Even at the young age of three she can tell the difference between a blob and a circle

or even an oval and a circle. We all have this intuitive understanding of circles,

but actually defining a circle is much more challenging.

Give it a try. Type your definition of a circle in this box.

Now compare your definition to mine and see how close you are.

A circle is defined as a 2-dimensional shape made by drawing a curve

that is always the same distance from a center.

As the distance from the centre of a circle is changed the size of the circle changes

but the shape does not. Adjust the distance from the centre and see how the circle changes.

The distance from the centre of the circle to edge is called:radius.

Mathematicians tend to use the small letter “r” to denote the radius of a circle.

We could draw a line directly through the centre of the circle.

This line is called the diameter and is defined as the distance from the edge of circle straight across the centre of the circle to the opposite edge.

A small “d” is used to denote diameter.

The diameter must cross the centre of the circle and be a straight line.

On this circle move the line until it becomes the diameter of the circle.

The distance around the edge of a circle is the circumference.

The small letter “c” is used to denote circumference.

The Legend of Archimedes: In ancient times, almost 2500 years ago,

a great scientist, mathematician and engineer lived by the name of Archimedes.

He is credited with many amazing discoveries.

For example he figured out that a screw in a tube could be used to pump water.

This picture shows how such a screw would bring a red ball up a tube.

In the same fashion water could be brought up the tube.

Archimedes used this device to pump water out of large wooden ships to prevent them from sinking.

This type of pump is still used today in many applications including coal mining.

Even more interesting is the legend that

Archimedes used the light reflected from mirrors to burn the ships of an attacking navy.

There has been many attempts to recreate this event including the one by the popular TV show, Mythbusters.

The mythbusters used 500 school children to point mirrors at a replica ship.

The ship did not catch on fire and Mythbusters declared this legend busted.

However, they did make the point that the mirrors could have been used to blind the ship’s crew while fiery arrows were shot,

so perhaps there was at least some truth to the legend.

There is another legend about Archimedes and an attacking army

that actually conquered the place where Archimedes lived.

When a solider attempted to capture Archimedes,

it has been reported that Archimedes was so engrossed in his math

(just like in this famous painting of Archimedes) that he did not pay any attention to the solider.

The frustrated solider drew his sword and killed Archimedes.

The legend says Archimedes uttered these final words: “do not disturb my circles.”

Whether these words were actually spoken is not one hundred percent certain

but Archimedes did demonstrate many properties of circles,

including proving the formula for area of a circle

and calculating the ratio of circumference to diameter very accurately.

Circle were very important to this legendary mathematician.

Introduction to Pi: In the first video I said that Archimedes very accurately calculated the ratio circumference to diameter of a circle.

This can also be written c over d because “c” denotes circumference and “d” denotes diameter.

The ratio c over d is called pi.

It sounds like the food but is spelt ”p” “i”.

We also use the Greek letter pi that looks like this to represent this ratio.

Pi is a very important ratio in math.

It turns out that no matter the size of a circle the ratio pi is always the same.

This is because as the diameter of a circle gets bigger

the circumference gets proportionally bigger.

Many people had estimated the value of pi before Archimedes.

An ancient Egyptian source estimated pi to be about 3.1605,

an ancient Indian source estimated pi to be 3.0883,

and a reference in the Bible estimates pi at 3.

Archimedes improved on all of these estimates

and demonstrated that pi was in-between 3.1408 and 3.1429.

It turns out pi is a very special number.

It has a decimal that goes on forever just like 0.3 repeating.

Unlike 0.3 repeating the decimal digits of pi go on forever without every repeating.

Here is pi to the fifty digits.

With the help of modern computers mathematicians have found the value of pi to 10 trillion digits and still there is no repeating pattern to the digits.

In fact getting super computers to calculate pi is one way to test the

computational power of a super computer.

For everyday math it is okay to estimate the value of pi to be 3.14.

So if you need pi to answer a question use the number 3.14.