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Alice’s adventures in inverse tan land – mathematical argument, language and proof
Paul Glaister
Journal:

The Mathematical Gazette / Volume 103 / Issue 558 / November 2019

Published online by Cambridge University Press:

21 October 2019, pp. 388-400

Print publication:

November 2019
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Andrew Palfreyman’s article [1] reminds us of the result (1)
$${\rm{ta}}{{\rm{n}}^{{\rm{ - 1}}}}{\rm{ + ta}}{{\rm{n}}^{{\rm{ - 1}}}}\,2{\rm{ + ta}}{{\rm{n}}^{{\rm{ - 1}}}}{\rm{ 3 = }}\,\pi {\rm{, }}$$
having been set the challenge of finding the value of the left-hand side by his head of department at the start of a departmental meeting.

Fibonacci power series
Paul Glaister
Journal:

The Mathematical Gazette / Volume 79 / Issue 486 / November 1995

Published online by Cambridge University Press:

01 August 2016, pp. 521-525

Print publication:

November 1995
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A student usually first meets power series through an infinite geometric progression, having previously considered finite geometric progressions. In this note we consider a variation of this introductory material which involves the Fibonacci numbers. This necessarily poses various questions, e.g. ’When does the series converge and, if so, what is the sum?’. However, there is one further intriguing question that is natural to ask, and this leads to some interesting mathematics. All of this is appropriate for sixth formers, either for classroom discussion or as an exercise.

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