Work

Re-presenting abstract and concrete in the diagrams of Al-Khwarizmi

Year: 2025

Type: conference-paper

Abstract: Al-Khwarizmi’s seminal and eponymous 9th century text on algebra, al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabalah (al-Jabr), has a number of diagrams which represent and support his algorithms for solving particular (families of) quadratic equations. In exploring these rectangular, area-based diagrams, which exemplify 'completing the square', we noticed that they disrupt the abstract-concrete dichotomy in mathematics and exemplify a more unified and inclusive approach to abstraction and concretisation in mathematics.

Source: Open Research Online (The Open University)

DOI: 10.1007/s42330-019

Authors: Maknaoui, Yassir, Kathotia, Vinay, Stenhouse, Brigitte

Institutions: University of London, The Open University

Language: English

Topic: History and Theory of Mathematics

Subfield: Theoretical Computer Science

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

OpenAlex ID: W7093348027