An introduction to the mathematics of the Golden Age of medieval Islam

This reading introduced several Islamic scientists and mathematicians including: al-Khwarizmi, al-Biruni, Umar al-Khayyami, and al-Kashi. Content from this week’s reading would be useful to use as a background to provide students when introducing topics on algebra or other related math topics.

It was interesting to learn more in-depth about al-Khwarizmi, as his name appeared in my individual math history research on exponents and powers. Al-Khwarizmi contributed to four areas of science: arithmetic, algebra, geography, and astronomy. From this reading, I noticed that many early mathematicians were astronomers. I also learned that algebra comes from the Arabic word al-jabr. As a math teacher, I think it would be interesting to teach a math lesson bridging with astronomy like how early mathematicians studied the stars. One idea I have could be for students to learn and trace out planetary orbit movements; we can tie an apple to a string and tape a marker to the apple and swing it over a piece of paper to map out it’s path of movement. From this activity, we can see interesting patterns form on the paper.

I learned that Umar al-Khayyami found that the ratio of the diagonal of a square to side (sqrt 2) and ratio of circumference of a circle to its diameter (π) and wanted to consider these as new kinds of numbers. These became known as irrational numbers. This history could be interesting to mention to students when teaching the number system. An idea I had was to design a “just for fun” assignment that get students to create their own way to classify and group numbers into a system like the number system. For example, students could great a classification for just prime numbers and another classification for numbers that at first glance look like prime numbers, when are in fact, composite numbers (eg. 2431).

Al-Khwarizmi and al-Kashi both correctly estimated the value of 2π to the first 16 decimal places. Al-Kashi solved a cubic equation to correctly obtain the value of sin(1^o) = 0.017452406… Al-Kashi developed a calculator method that can repeat a procedure each time using the previous result to obtain numbers near the true value of the root of an equation. This reminds me of Euler’s method, which a technique used to analyze a differential equation using the idea of linear approximation by calculating the result using the previous result.

 

Reading:

Berggren, J.L. (2016). Episodes in the Mathematics of Medieval Islam. Springer. 2nd Edition. 1-23.