In this workshop we develop the continued fraction expansion of a number compared with its decimal expansion. All operations involve the manipulation of fractions.
In the first instance it appears a strange way to represent numbers. However it soon becomes apparent that numbers, such as √2 have a very simple continued fraction expansion compared with their decimal representation.
The wonderful Indian mathematician Srinivasa Ramanujan was a master at the use of continued fractions as approximations to numbers such as π.
We shall start the workshop by showing how the real number system is comprised of integers, rational and irrational numbers. Then further breakdown of the irrationals into algebraic and transcendental numbers.
SECONDARY: continued fraction expansion of rational and irrational numbers, representation of continued fraction as a rational or irrational number, a surprisingly simple representation of √2
SIXTH FORM: plus Khinchin’s constant, some theorems and proofs.
Copyright Maths Discovery 2015