Despite the fact that the 14th March is not expressed as 3.14 in the UK and many other countries, it is still worth giving some attention to this irrational number on Pi Day, which takes place on Wednesday. Here are approximately three activities – other than eating pie – that can be used in your classroom.
Is 3.14 an irrational number?
Explain that irrational numbers cannot be expressed as a ratio (do they notice the hint in the name?) Ask students whether 3.14 is an irrational number. If they need a hint, ask them to think about whether they can think of a fraction which is equal to 3.14. They could use 314/100 which is equivalent to 157/50. This task will be easier if students are used to connecting fractions with division.
Radius and Circumference Estimates
Show pupils a circular object, and in their groups, they have to estimate the radius and circumference of the circle. This activity can be used before students are aware of the connection between the diameter and the circumference. In this case, it can be used to help pupils to discover that the length of the circumference is always slightly more than three times the length of the diameter, in all circles, regardless of their size.
Following time for discussion, each group provides their estimates as ranges. Explain that units must be provided and that the correct measured length must fall within their range. Also, for those that qualify, the group that provides the narrowest range wins.
Some time could also be spent discussing how they are going to measure the circumference of the given circle. Pupils may suggest string, tape measures, or marking a point on the circumference and rolling the circle along a straight line or a ruler and marking the length where the marked point is reached.
If this is repeated several times, pupils should start to notice that the measured circumferences are always approximately three times bigger than the diameters of the circles.
How long would it take to recite Pi to 100,000 decimal places?
In 2006, Akira Haraguchi, a Japanese man, recited pi to 100,000 decimal places.
Ask pupils to estimate how long this would take. Provide them with the first 50 digits of pi. Group members could then be timed reading these decimal places out loud for a certain number of seconds or timed to see how long it takes them to read all 50 decimal places. Based on the results, the group can then estimate how many digits they could read in one minute.
This could then be compared to the feat mentioned above where a Japanese man took over 16 hours to recite 100,000 digits. Ask pupils to work out the approximate number of digits recited for a certain length of time which can then be compared with the number of digits read by their group members in the same amount of time. How long would it take them to read 100,000 digits?
Pi to 50 digits:
Where can my birthday be found within π digits?
This is the extra bit activity since it doesn’t require any maths but is a bit of fun!
www.mypiday.com allows you to enter a date or any string of numbers in order to find where they sit within the digits of pi. It does give pupils a feel for the massive number of digits involved.
To download a free PowerPoint Presentation containing all these activities, visit www.mathsmoves.co.uk/teacherresources
Alternative dates for celebrations.
If celebrating Pi Day on March 14th does not feel right to you, then don’t worry - there is another opportunity: Pi Approximation Day is held on 22nd July since this date represents 22/7. Alternatively, you could forget Pi altogether and focus on Tau Day. Tau represents the ratio of the circumference to the radius of a circle and is approximately 6.28, although this again has to be expressed in US date format since it takes place on June 28th.
Enjoy your π day celebrations.