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Iam reading Julian Havil's book, The Irrationals: A Story of the Numbers You Can't Count On.
In Chapter 3 Havil is writing about progress in the eighteenth century in determining the nature of $$\pi$$ and $$e$$ through the use of continued fractions. He writes (pages 92 - 93):View attachment 2851
View attachment 2852
Can someone please explain how one can determine/show $$\pi$$ as a continued fraction: that is how is the expression for $$\pi$$ given at the bottom of the page derived - what is the method of derivation?
Peter
In Chapter 3 Havil is writing about progress in the eighteenth century in determining the nature of $$\pi$$ and $$e$$ through the use of continued fractions. He writes (pages 92 - 93):View attachment 2851
View attachment 2852
Can someone please explain how one can determine/show $$\pi$$ as a continued fraction: that is how is the expression for $$\pi$$ given at the bottom of the page derived - what is the method of derivation?
Peter