(KS3, Year 7)
The LessonPi is mathematical constant, denoted by the symbol π. Pi is approximately equal to:
Dictionary DefinitionThe 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 22⁄7. Usually written π."
Pi Is the Ratio of Circumference to DiameterPi 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?
GeometryPi 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.
- 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.
TrigonometryPi 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 PiPi 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 ForeverPi is an irrational number; it cannot be expressed as a ratio of two numbers. Because of this, Pi goes on forever.
22 / 7As 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
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