Saturday 14 March is recognised as an important day in mathematical circles. It is celebrated around the world as Pi Day.

When students are asked to reflect on what they know about the number pi, they usually respond with “pi is about circles and stuff”. But this value is more than just a number that relates to circles – it is a natural phenomenon. The value and use of pi should never be underestimated as it is used in building and construction calculations, quantum physics, communications, music theory, medical procedures, air and space travel, just to name a few.

Since the history of time there has been much speculation and excitement surrounding this irrational number. Mathematics Professor and author William L. Schaaf once said, “Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi”.

Many have pondered its worth, from the ancient Babylonians to the scholars from the Middle Ages in Europe, to the supercomputers of today. Many have searched for approximations of this number using rational numbers, formulas, and more recently, patterns in the infinite line of numbers which is generally shortened to 3.142. Defined as a transcendental, a number that can only be expressed as a decimal, one that never ends and never repeats. This number still captures our minds and interest.

In simple terms, pi is equivalent to the circumference of any perfect circle divided by the length of its diameter. This year, many of our Year 9 students will be embarking on the journey that is Trigonometry, and will learn that tan(45°) = 1.

When we work with angles expressed in radians, this same equation looks slightly different, that is,

Our skills at secondary school may be slightly limited but with the aid of an Excel Spreadsheet or possibly an algorithm, students will be able to approximate the value of pi.

A Taylor Series is used to do so. The basic premise behind a Taylor Series is that any function looks like a power series if we focus on one part of that function.

Using

which can be manipulated to

this Taylor Series at the x = 1 point is now:

This technique is not necessarily the most efficient means to approximating the value of pi but one that our students could begin using when trying to gain an understanding.

So with this I add a happy belated Pi Day everybody and enjoy approximating!