Pi
(KS3, Year 7)

The Lesson

Pi is mathematical constant, denoted by the symbol π. Pi is approximately equal to:

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Pi Is the Ratio of Circumference to Diameter

Pi is the ratio of a circle's circumference to its diameter.

In this formula, C is the circumference and d is the diameter. This ratio is constant for all circles.

Why Is Pi Useful?

Geometry

Pi is useful in the geometry of circular shapes.

• The circumference of a circle with radius r is 2πr.
• The area of a circle with radius r is πr².
• The surface area of a circle with radius r is 4πr².
• The volume of a sphere with radius r is ⁴/₃πr³.

Cones and cylinders also contain circles. Pi is useful in finding their volumes.

• The volume of a cone with height h and base radius r is ¹/₃πr²h.
• The volume of a cylinder with height h and base radius r is πr²h.

Trigonometry

Pi is found in trigonometry because the sine, cosine and tangent functions can be defined from a unit circle. Sine and cosine functions can be used to describe signals, like alternating currents and radio waves. This means π is often used when analysing signals, such as finding the power coming from a mains supply.

The Value of Pi

Pi has been known since ancient times. Its value was known to reasonable accuracy as just over 3. Over the centuries, many mathematicians, such as Archimedes, have found ways of finding π to more and more decimal places. Now we have computers, π is known to trillions of digits.

Pi Goes On Forever

Pi is an irrational number; it cannot be expressed as a ratio of two numbers. Because of this, Pi goes on forever.

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As Pi is irrational, it cannot be expressed as a fraction. However, it can be approximated by ²²⁄₇. ²²⁄₇ = 3.14285, which is slightly larger than π = 3.14159.

The Pi Pie