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Alice’s adventures in inverse tan land – mathematical argument, language and proof

Published online by Cambridge University Press:  21 October 2019

Paul Glaister
Paul Glaister*
Affiliation:
Department of Mathematics, University of Reading, Reading e-mail: p.glaister@reading.ac.uk
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Extract

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.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 558 , November 2019 , pp. 388 - 400
Copyright
© Mathematical Association 2019 

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References

Palfreyman, A., Inverse tan does it add up to anything?, Mathematics in School, 47(1) (2018) pp. 24-25.Google Scholar
Abeles, F. F., Charles, L. Dodgson’s geometric approach to arctangent relations for pi, Historia Mathematica, 20 (1993) pp. 151-159, also available at http://users.uoa.gr/~apgiannop/Sources/Dodgson-pi.pdf 10.1006/hmat.1993.1013CrossRefGoogle Scholar
Department for Education, GCE AS and A level subject content for mathematics (2014) also available at https://www.gov.uk/government/publications/gce-as-and-a-level-mathematicsGoogle Scholar