Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom - More Ideas for Activities and Projects

Download the three modules discussed in this article:

• Combinations and Their Sums (Elementary Statistics, Finite Mathematics)
• Binomial Coefficients and Subsets (Finite Mathematics)
• Using the Derivative to Solve an Optimization Problem (Calculus for Business and Social Sciences)

Besides the topics addressed in these modules, other topics from Islamic mathematics that can be adapted for classroom activities or student projects include:

• double false position (hisāb al-khatā’ayn), an arithmetical procedure for evaluating linearly related quantities (Chabert 1999: 83-112; Schwartz forthcoming; cf. Shen et al. 1999: 349-385 and Sigler 2002: 447-487).
  Download modules on this topic:
  The Rule of Double False Position (Calculus for Business and Social Sciences)
  The Rule of Double False Position (Linear Algebra)
• the use of arithmetical and algebraic techniques for the Qur’ānic division of estates and the calculation of alms taxes (Berggren 1986: 63-68; Lesser 2000: 63; Rosen 1831: 86-174)
• the use of spherical trigonometry in determining the times for Islamic holidays and the five daily prayers, as well as the qibla or prayer direction facing Mecca (Berggren 1986: 157-186; Katz 2009: 306-317; Van Brummelen 2009: 170-172, 192-201)
• the geometry of patterns used in the design and decoration of mosques and palaces (Niman and Norman 1978; Özdural 2000)
• combinatorial and inductive techniques that lead toward integral calculus (Katz 1995)
• discoveries in number theory resulting from the search for perfect, abundant, deficient, and amicable numbers (Rashed 1994: 277-287).

The practical needs of Islam, reflected in the above list, were among the reasons that the spread of this faith stimulated mathematical work in the Middle Ages. More fundamental was the impact of its central doctrine of al-tawhīd, variously translated as “unification” or “unity in multiplicity.” This doctrine encouraged a sweeping embrace of all knowledge and all people as the best way to know God (Schwartz 2001). In a multicultural society such as ours, the outlook of unity in multiplicity has great relevance to education. The work described in this article shows that in a classroom consciously based on global diversity, students not only learn more mathematics, they learn how every culture has important contributions to make to the unified stock of human knowledge.