Funmaths

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.

 

Diameter and 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.

 

Pi

 

 

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:

3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803 48253421170679821480865132823066470938446095 50582231725359408128481117450284102701938521 10555964462294895493038196442881097566593344 61284756482337867831652712019091456485669234 60348610454326648213393607260249141273724587 00660631558817488152092096282925409171536436 78925903600113305305488204665213841469519415 11609433057270365759591953092186117381932611 79310511854807446237996274956735188575272489 12279381830119491298336733624406566430860213 94946395224737190702179860943702770539217176 29317675238467481846766940513200056812714526 35608277857713427577896091736371787214684409 01224953430146549585371050792279689258923542 01995611212902196086403441815981362977477130 99605187072113499999983729780499510597317328 16096318595024459455346908302642522308253344 68503526193118817101000313783875288658753320 83814206171776691473035982534904287554687311 59562863882353787593751957781857780532171226
806613001927876611195909216420198

 

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.

 

Value of Pi

 

Using 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.

 

Using Pi

 

If your calculator doesn't have a Pi key, then use the approximate value of Pi as 3.142

 

For you to try...

  1. 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?
  2. The moon has a diameter of 3480km. How long is it's circumference?
  3. 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?

 

Answers:

1. 15.7cm

2. 10 932.74km

3. 48 000km ; 1 319km