Amaze your pupils with the power of this mystical number, says Stephen Froggatt
Next Friday is a rather special date. The month (3) and the day (14) give us 3.14, which is pi to two decimal places. That's enough for teachers around the world to mark it as International Pi Day.
What is pi? Simply put, it is the number you get when you divide any circle's circumference by its diameter.
It's the same number throughout the universe, and throughout time, and remains one of the few topics of ancient mathematics that still intrigue mathematicians today. It is useful in many contexts. If you are a mathematically inclined cook, you can multiply the width of your circular cake tin by pi to find the length of ribbon needed to go round your cake. But if cars and bikes are more your thing, you can be sure that doubling the size of a wheel will double the distance travelled in one revolution - because pi is the same for every circle. It even explains how gears work.
Amaze your pupils by telling them that a value of pi correct to only 50 places (above) is sufficient to calculate the circumference of the known universe to a precision equivalent to the width of a hydrogen atom. Yet that hasn't stopped people wanting to know more. Ever since the ancient Egyptians, people have tried to calculate pi with greater and greater accuracy, but even with today's most powerful computer we only know the first trillion places or so. Pi is an irrational number, going on forever without repeating, so we are no closer to "the end" than we were before.
Here are some ideas to try in your classroom to celebrate International Pi Day this year:
- Measure it. Find a large collection of circular objects, using string to measure the circumference, and divide this by the diameter. How close were you?
- Research it. Find out about early attempts to measure and calculate pi and mark these on a history timeline.
- Learn it. Surprisingly easy and maddeningly addictive, pupils of any age quickly find that they can recite 15 places or 25 places, venturing past the "uselessness barrier" of 50 places and on into 100 places or more. A Year 7 pupil of mine once learnt 200 places in an evening.
- Calculate it. Can you find a fraction better than 227 for giving you digits of pi? Can you use pi on your calculator to work out diameters, circumferences and areas of circles? Can you use an infinite series on a spreadsheet to find pi to even more places than your calculator?
- Hear it. Convert digits into notes and play the tune within pi.
- Act it. Long chains of people make good lengths. If you have a line of five similarly sized people finger-tip to finger-tip as your diameter, then you will find you need about 16 other people to make the circle around them.
- Display it. Make a large paper chain where each loop represents one digit (perhaps colour-coded) and snake it around the school.
Of course, the only one we haven't considered in that list is "Eat it!" Perhaps that would come first in many teachers' and pupils' suggestions. And why not? Keep an eye on the clock though. 3rd Month. 14th Day. 1:59pm and 26 seconds: everyone solemnly eats a piece of pie and vows to meet again in Pi-sa for World Pi Approximation Day.
That's on July 22, but of course you know that already.
Stephen Froggatt is head of maths at Oaks Park High School in Ilford, Essex. Visit www.mathsisfun.netmemoryPi.htm.