Second talk at the Diversifying the curriculum conference in Oxford.

The following was taken down live, and as such there may be mistakes and misquotes. It is mostly a way for me to keep notes and to share useful resources and thoughts with others. As such, nothing should be used to quote the speaker from this article

How to generate interesting conversations with students surrounding mathematical diversity.

**Historical figures (From wikipedia):**

Omar Khayyam18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet. He was born in Nishapur, in northeastern Iran, and spent most of his life near the court of the Karakhanid and Seljuq rulers in the period which witnessed the First Crusade.As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics.

Oliver Byrne(31 July 1810 – 9 December 1880) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering. He is best known for his ‘coloured’ book of Euclid‘sElements.

This talk was in part motivated by taking Byrne’s methods of explication and taking them in a slightly more modern direction (for instance, with the use of Geogebra).

Oliver Byrne, in around 1847, wrote “*The First Six Books of the Elements of Euclid in which Coloured Diagrams and Symbols Are Used instead of Letters for the Greater Ease of Learners.”*

Page taken from here:

New editions of Byrne coming out now.

Edward Tufte – the visual display of quantitative information

From Byrne:

We are happy to find that the Elements of Mathematics now forms a considerable part of every sound female education, therefore we call the attention to those interested or engaged in the education of ladies to this very attractive mode of communicating knowledge, and to the succeeding work for its future development.

Statistics from catalyst.org – data on women in stem. Once women enter STEM they are 45% more likely to leave than men.

Can we combine Byrne’s very graphical methods to prove Omar Khayyam’s solution of the cubics?

The construction is a geometric one, involving lines, rectangles and boxes and proving the equation for the solution of a cubic using these.

This is a Geogebra page showing the solution of the cubic without the Byrne inspired construction.

**Comment:** Useful as a way of showing that there are multiple ways of tackling the same problem.

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