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 is used in calculations. What is it about π that causes problems? Students from an early age learn that π is the ratio of the circumference of a circle to its diameter and so this reinforces the geometrical interpretation of π. However, π 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 into revolutions or degrees just because of the connection of π 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 seconds and many candidates lost marks by converting this into degrees.
βThe fact that π, 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 activityβ
