The number π has been of interest to mathematicians for more than 4000 years. It was certainly known to the Babylonians, the Egyptians and the Chinese so 1000 years BC. The first person to make a serious mathematical study was Archimedes who developed a technique very similar to those that we use today, predating the modern developers by nearly 2000 years. We shall follow Archimedes and use his geometrical technique to obtain an approximation to π.
We shall describe our number system and see that as well as the integers an fractions we require the irrationals to complete the set. In particular we shall discover a subset of the irrationals called the transcendental numbers to which π belongs. Finally we shall look at the decimal expansion and investigate whether or not it is random. The workshop will develop as a chronology of π and will involve the solution of a wide variety of problems where we shall see that π crops up in some unexpected paces.
PRIMARY: practical measurements to develop the circumference /diameter relationship of a circle,
brief introduction to irrational numbers, ‘where’s my birthday in π?’
SECONDARY: plus Archimedes’ inscribed/circumscribed polygon approximation for π, introduction
to transcendental numbers.
SIXTH FORM: plus development of real number system, ubiquity of transcendental numbers,
extrapolation techniques for improving estimates.
Copyright Maths Discovery 2015