Filling in the short blanks: musings on bringing the historiography of mathematics to the classroom

Abstract

Writing a history of early trigonometry brought me to confront in a practical way some difficult historiographic questions. What does it mean to know a theorem? How does one determine what belongs to trigonometry, and doesn't? To what extent can one legitimately talk about knowledge crossing cultural boundaries intact? Although these questions do not have clear answers, their introduction to a classroom setting could enrich and deepen students' perceptions of what mathematics is, and how culture interacts with it.

Acknowledgements

The author is grateful for comments and suggestions by Ryan Derby-Talbot, Yousuf Kerai, and Bob Stein. All remaining deficiencies are, as usual, my responsibility.

Notes

¹ This phrase is used deliberately. Thomas Kuhn's ‘The essential tension’ (Kuhn 1977, 225–239) explores the conflict between innovation and tradition in scientific practice, and it seems to me that something similar is at work here—a tension between tradition and innovation in the use of history in the mathematics classroom.

² The obtuse-angled case is handled in the previous proposition, II.12.

³ The cover of Eli Maor's Trigonometric delights (Maor 1998), for instance, is graced with a photograph of the Pyramid at Giza and the Sphinx. To be fair, however, Maor refers to Egyptian triangle calculations as ‘proto-trigonometry’.

⁴ In Michael's text this angle is given as 2 ‘quarters’, where 8 quarters compose a right angle.

⁵ This apparently innocuous claim is made in Kelley 2000, 43–45.

⁶ Bj⊘rn Smestad, http://bjornsmaths.blogspot.com/2008_08_01_archive.html. Accessed August 25, 2009.

⁷ The alargar and ritorno are the names given by marteloio practitioners to tables mathematically equivalent to our sine and its reciprocal.