Pi......From a Student's Perspective

Examiners in the HSC Advanced Mathematics (2 unit) course have commented that many students become confused when the constant πœ‹ is used in calculations. What is it about πœ‹ that causes problems? Students from an early age learn that πœ‹ is the ratio of the circumference of a circle to its diameter and so this reinforces the geometrical interpretation of πœ‹. However, πœ‹ can be involved in problems that have no connection with circles and this is when confusion in examination answers can arise. Some students convert an answer involving πœ‹ into revolutions or degrees just because of the  connection of πœ‹ to the geometry of a circle. Pi is a number, an irrational number, and should be treated like any other number in calculations. In the 2015 Mathematics examination question 15 c involved calculating the time when the volume of water in a pool first started to decrease given the rate of change of the volume. The answer was 2πœ‹ seconds and many candidates lost marks by converting this into degrees.

The fact that πœ‹, a purely geometric ratio, could be evolved out of so many arithmetic relationships- out of infinite series, with apparently little or no relation to geometry-was a never ending source of wonder and a never ending stimulus to mathematical activity
— Mathematics and the Imagination by Edward Kasner and James Newman, G Bell and Sons 1951, page 78