What Is a Circle?
Before we dive into calculations, let's make sure we're on the same page about what a circle actually is and the key parts we'll be working with.
A circle is a perfectly round shape where every point on the edge is exactly the same distance from the centre.
A set of all points in a plane that are equidistant (the same distance) from a fixed centre point.
The distance from the centre of a circle to any point on its edge. Often written as .
The distance across a circle, passing through the centre. It is exactly twice the radius: .
The perimeter of a circle — the total distance around the outside edge.
The amount of two-dimensional space enclosed inside the circle.
Think of a circle like a bicycle wheel. The radius is a single spoke from the hub to the rim. The diameter is a spoke that goes all the way across, passing through the hub. The circumference is the distance the tyre covers in exactly one full rotation.
Introducing Pi (π)
There is a special number that connects every circle's circumference to its diameter. That number is called pi.
The ratio of a circle's circumference to its diameter. It is an irrational number (its decimal digits never end and never repeat).
No matter how big or small a circle is, if you divide its circumference by its diameter, you always get π:
This means:
People discovered this relationship thousands of years ago — ancient Babylonians and Egyptians both estimated π. Today we can calculate trillions of its decimal places, but for most problems we use:
- (for quick estimates)
- (for more accuracy)
- The button on your calculator (for the best accuracy)
In MYP assessments, unless the question says otherwise, use the π button on your calculator and round your final answer to the number of decimal places or significant figures asked for.
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