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

Image source: https://musliminitiators.files.wordpress.com/2016/03/muslim-contributions-in-mathematics-4-638.jpg?w=387&h=290

I first just want to say how excited I was about this reading and I appreciated that we were assigned reading that included a bit of background regarding the beginnings of Islam as well. I have taken first year Religious Studies as well as a handful of Asian Studies courses so it was very cool to recognize some of the groups and important figures being mentioned.

One of the main things that stood out to me was how a few of these mathematicians were not solely famous for their work in the field of math. For example, Thabit ibn Qurra was skilled at languages and a translator as well as someone who studied math. Al-Biruni similarly acted as a mediator in political affairs on top of his work in math and 'Umar was famous for his poetry. If we make these connections with our students, we can break the stereotype that I believe is attached to mathematicians - that they are these anti-social, studious people who lock themselves in their offices to create works of genius. For example, I looked up 'Umar al-Khayyami, found that another Anglicization of his name is "Omar Khayyam," and found that one of my favourite singers had sung one of his poems on Coke Studio Pakistan. Instantly, it felt like this figure was brought to life for me, instead of just being some famous mathematician from the past. Even though his work in mathematics is impressive in itself, learning more about the person as a whole helps to make learning about them that more interesting and impactful.

Another thing I found interesting was how al-Biruni (along with Abu al-Wafa) used an eclipse of the moon to find the longitude difference between Kath and Baghdad. This was an interesting method I had not heard of before and, according to Encyclopedia.com, "...the findings of al-Biruni and Abu al-Wafa represented one of the few instances in which accurate longitudinal calculations were made in the premodern period." This would be a good example to bring up with students because its findings are more tangible and they may be able to visualize this. Again, it feeds into the idea of bringing math and history to life and hopefully sparks wonder into some students as to how they may have gone about doing that.

I think one of the most mind-blowing parts of this reading was that al-Kashi was able to accurately calculate 2*pi to sixteen decimal places, and that he knew exactly what he was aiming for. Not only that, but, "...he calculated the perimeters of inscribed and circumscribed polygons, in a given circle, having 805,306,368 sides." The amount of careful planning and dedication that this mathematician had is extraordinary! In searching more into this, I found that, in an article from 2016, NASA mentions that they only use a 15 decimal approximation of pi. That means al-Kashi in 1424 found an accuracy that went a long way in helping astronomers throughout history. I checked my graphing calculator (which of course, I'm only using for simple calculations anyway) and it only rounds to 9 decimal places. This story not only highlights the impressive work of an ancient mathematician, but also can be used to relate the extent of that discovery by comparing it to modern uses of pi and our students' own use of their calculators. It's also, in my opinion, a great story for showing perseverance - especially if we mention that al-Kashi's goal was to be accurate within the "width of a horse's hair" to the true value of the "circumference of the universe according to ancient dimensions."