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Pi
(KS3, Year 7)
The Lesson
Pi is mathematical constant, denoted by the symbol π. Pi is approximately equal to: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 ^{22}⁄_{7}. Usually written π."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 πr^{2}.
- The surface area of a circle with radius r is 4πr^{2}.
- The volume of a sphere with radius r is ^{4}/_{3}πr^{3}.
- The volume of a cone with height h and base radius r is ^{1}/_{3}πr^{2}h.
- The volume of a cylinder with height h and base radius r is πr^{2}h.
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 ^{22}⁄_{7}. ^{22}⁄_{7} = 3.14285, which is slightly larger than π = 3.14159.The Pi Pie
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