What is Pi?
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People have know for a long time about the relationship between the circumference and diameter of a circle. They've know that if you take the diameter of a circle and multiply it by 3 and a bit you get the circumference.
This number, the 3 and a bit, is represented by the Greek letter Pi (pronounced pie). Mathematicians started using this symbol to represent Pi in the 1700s. You can see what pie looks like below.
But 3 and a bit is not very accurate. Pi is approximately 3.14159. Even that is not accurate. How much is it exactly?
Pi is an irrational number and this means the number of decimals after the point never ends. Modern computers have calculated the value of Pi to over a trillion decimal places and it appears the digits are randomly distributed. But the exact value of Pi is still not known.
The first 500 digits of Pi:
Ways of showing Pi
Over the centuaries, different mathematicians suggested different ways of representing the value of Pi. Pi has been known for almost 4000 years. Ancient civilisations need Pi for building and other practical reasons. The Babylonians calculated the area of circle by squaring the radius and multiplying that by 3. That means they gave Pi a value of 3.
The first person to calculate Pi was Archimedes (287 - 212 BC). He showed that Pi was between 3 1/7 and 3 10/71. Convert those fractions on your calculator to compare them to the first 500 digits above.
A Chinese mathematician named Zu Chongzhi (429 - 501 AD) used the fraction 355/113.
Even today, most calculations only need Pi to 40 places. Here are some old and new ways to show the value of Pi.
If you know the diameter of a circle, you can use Pi to calculate the circumference. First you'll need to find the Pi symbol on your calculator.
If your calculator doesn't have a Pi key, then use the approximate value of Pi as 3.142
For you to try...
- Your grandmother has made a bottle of homemade jam. She'd like you to make a label for the bottle. If the bottle has a diameter of 5cm, how long will the label need to be?
- The moon has a diameter of 3480km. How long is it's circumference?
- A satellite orbits the earth (diameter 12640km). It completes one orbit in 24 hours. If it's speed is 2000km/hr, how far does it travel in one orbit? And how far from the earth is it?
2. 10 932.74km
3. 48 000km ; 1 319km