Pi
(KS3, Year 7)

The Lesson

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

pi equals 3.14159

Dictionary Definition

The Oxford English Dictionary defines pi as "a transcendental number which is equal to the ratio of the circumference of a circle to the diameter, having a decimal form beginning 3.14159265…, and commonly approximated to 227. Usually written π."
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Pi Is the Ratio of Circumference to Diameter

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

pi equals circumference divided by 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.

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.
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170...

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.

22 / 7

As Pi is irrational, it cannot be expressed as a fraction. However, it can be approximated by 227. 227 = 3.14285, which is slightly larger than π = 3.14159.

The Pi Pie

pi written on a pie
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See Also

What is a circle? Finding the area of a circle Finding the volume of a sphere Finding the volume of a cone Finding the volume of a cylinder Archimedes What is the sine function? What is the cosine function? What is the tangent function?